Project acronym ALOGLADIS
Project From Anderson localization to Bose, Fermi and spin glasses in disordered ultracold gases
Researcher (PI) Laurent Sanchez-Palencia
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Starting Grant (StG), PE2, ERC-2010-StG_20091028
Summary The field of disordered quantum gases is developing rapidly. Dramatic progress has been achieved recently and first experimental observation of one-dimensional Anderson localization (AL) of matterwaves has been reported using Bose-Einstein condensates in controlled disorder (in our group at Institut d'Optique and at LENS; Nature, 2008). This dramatic success results from joint theoretical and experimental efforts, we have contributed to. Most importantly, it opens unprecedented routes to pursue several outstanding challenges in the multidisciplinary field of disordered systems, which, after fifty years of Anderson localization, is more active than ever.
This theoretical project aims at further developing the emerging field of disordered quantum gases towards novel challenges. Our aim is twofold. First, we will propose and analyze schemes where experiments on ultracold atoms can address unsolved issues: AL in dimensions higher than one, effects of inter-atomic interactions on AL, strongly-correlated disordered gases and quantum simulators for spin systems (spin glasses). Second, by taking into account specific features of ultracold atoms, beyond standard toy-models, we will raise and study new questions which have not been addressed before (eg long-range correlations of speckle potentials, finite-size effects, controlled interactions). Both aspects would open new frontiers to disordered quantum gases and offer new possibilities to shed new light on highly debated issues.
Our main concerns are thus to (i) study situations relevant to experiments, (ii) develop new approaches, applicable to ultracold atoms, (iii) identify key observables, and (iv) propose new challenging experiments. In this project, we will benefit from the original situation of our theory team: It is independent but forms part of a larger group (lead by A. Aspect), which is a world-leader in experiments on disordered quantum gases, we have already developed close collaborative relationship with.
Summary
The field of disordered quantum gases is developing rapidly. Dramatic progress has been achieved recently and first experimental observation of one-dimensional Anderson localization (AL) of matterwaves has been reported using Bose-Einstein condensates in controlled disorder (in our group at Institut d'Optique and at LENS; Nature, 2008). This dramatic success results from joint theoretical and experimental efforts, we have contributed to. Most importantly, it opens unprecedented routes to pursue several outstanding challenges in the multidisciplinary field of disordered systems, which, after fifty years of Anderson localization, is more active than ever.
This theoretical project aims at further developing the emerging field of disordered quantum gases towards novel challenges. Our aim is twofold. First, we will propose and analyze schemes where experiments on ultracold atoms can address unsolved issues: AL in dimensions higher than one, effects of inter-atomic interactions on AL, strongly-correlated disordered gases and quantum simulators for spin systems (spin glasses). Second, by taking into account specific features of ultracold atoms, beyond standard toy-models, we will raise and study new questions which have not been addressed before (eg long-range correlations of speckle potentials, finite-size effects, controlled interactions). Both aspects would open new frontiers to disordered quantum gases and offer new possibilities to shed new light on highly debated issues.
Our main concerns are thus to (i) study situations relevant to experiments, (ii) develop new approaches, applicable to ultracold atoms, (iii) identify key observables, and (iv) propose new challenging experiments. In this project, we will benefit from the original situation of our theory team: It is independent but forms part of a larger group (lead by A. Aspect), which is a world-leader in experiments on disordered quantum gases, we have already developed close collaborative relationship with.
Max ERC Funding
985 200 €
Duration
Start date: 2011-01-01, End date: 2015-12-31
Project acronym CPDENL
Project Control of partial differential equations and nonlinearity
Researcher (PI) Jean-Michel Coron
Host Institution (HI) UNIVERSITE PIERRE ET MARIE CURIE - PARIS 6
Call Details Advanced Grant (AdG), PE1, ERC-2010-AdG_20100224
Summary The aim of this 5,5 years project is to create around the PI a research group on the control of systems modeled by partial differential equations at the Laboratory Jacques-Louis Lions of the UPMC and to develop with this group an intensive research activity focused on nonlinear phenomena.
With the ERC grant, the PI plans to hire post-doc fellows and PhD students, to offer 1-to-3 months positions to confirmed researchers, a regular seminar and workshops.
A lot is known on finite dimensional control systems and linear control systems modeled by partial differential equations. Much less is known for nonlinear control systems modeled by partial differential equations. In particular, in many important cases, one does not know how to use the classical iterated Lie brackets which are so useful to deal with nonlinear control systems in finite dimension.
In this project, the PI plans to develop, with the research group, methods to deal with the problems of controllability and of stabilization for nonlinear systems modeled by partial differential equations, in the case where the nonlinearity plays a crucial role. This is for example the case where the linearized control system around the equilibrium of interest is not controllable or not stabilizable. This is also the case when the nonlinearity is too big at infinity and one looks for global results. This is also the case if the nonlinearity contains too many derivatives. The PI has already introduced some methods to deal with these cases, but a lot remains to be done. Indeed, many natural important and challenging problems are still open. Precise examples, often coming from physics, are given in this proposal.
Summary
The aim of this 5,5 years project is to create around the PI a research group on the control of systems modeled by partial differential equations at the Laboratory Jacques-Louis Lions of the UPMC and to develop with this group an intensive research activity focused on nonlinear phenomena.
With the ERC grant, the PI plans to hire post-doc fellows and PhD students, to offer 1-to-3 months positions to confirmed researchers, a regular seminar and workshops.
A lot is known on finite dimensional control systems and linear control systems modeled by partial differential equations. Much less is known for nonlinear control systems modeled by partial differential equations. In particular, in many important cases, one does not know how to use the classical iterated Lie brackets which are so useful to deal with nonlinear control systems in finite dimension.
In this project, the PI plans to develop, with the research group, methods to deal with the problems of controllability and of stabilization for nonlinear systems modeled by partial differential equations, in the case where the nonlinearity plays a crucial role. This is for example the case where the linearized control system around the equilibrium of interest is not controllable or not stabilizable. This is also the case when the nonlinearity is too big at infinity and one looks for global results. This is also the case if the nonlinearity contains too many derivatives. The PI has already introduced some methods to deal with these cases, but a lot remains to be done. Indeed, many natural important and challenging problems are still open. Precise examples, often coming from physics, are given in this proposal.
Max ERC Funding
1 403 100 €
Duration
Start date: 2011-05-01, End date: 2016-09-30
Project acronym DISPEQ
Project Qualitative study of nonlinear dispersive equations
Researcher (PI) Nikolay Tzvetkov
Host Institution (HI) UNIVERSITE DE CERGY-PONTOISE
Call Details Starting Grant (StG), PE1, ERC-2010-StG_20091028
Summary We plan to further improve the understanding of the nonlinear dispersive wave propagation phenomena. In particular we plan to develop tools allowing to make a statistical description of the corresponding flows and methods to study transverse stability independently of the very particular arguments based on the inverse scattering. We also plan to study critical problems in strongly non Euclidean geometries.
Summary
We plan to further improve the understanding of the nonlinear dispersive wave propagation phenomena. In particular we plan to develop tools allowing to make a statistical description of the corresponding flows and methods to study transverse stability independently of the very particular arguments based on the inverse scattering. We also plan to study critical problems in strongly non Euclidean geometries.
Max ERC Funding
880 270 €
Duration
Start date: 2010-10-01, End date: 2015-09-30
Project acronym GMODGAMMADYNAMICS
Project Dynamics on homogeneous spaces, spectra and arithmetic
Researcher (PI) Elon Lindenstrauss
Host Institution (HI) THE HEBREW UNIVERSITY OF JERUSALEM
Call Details Advanced Grant (AdG), PE1, ERC-2010-AdG_20100224
Summary We consider the dynamics of actions on homogeneous spaces of algebraic groups,
We propose to tackle the central open problems in the area, including understanding actions of diagonal groups on homogeneous spaces without an entropy assumption, a related conjecture of Furstenberg about measures on R / Z invariant under multiplication by 2 and 3, and obtaining a quantitative understanding of equidistribution properties of unipotent flows and groups generated by unipotents.
This has applications in arithmetic, Diophantine approximations, the spectral theory of homogeneous spaces, mathematical physics, and other fields. Connections to arithmetic combinatorics will be pursued.
Summary
We consider the dynamics of actions on homogeneous spaces of algebraic groups,
We propose to tackle the central open problems in the area, including understanding actions of diagonal groups on homogeneous spaces without an entropy assumption, a related conjecture of Furstenberg about measures on R / Z invariant under multiplication by 2 and 3, and obtaining a quantitative understanding of equidistribution properties of unipotent flows and groups generated by unipotents.
This has applications in arithmetic, Diophantine approximations, the spectral theory of homogeneous spaces, mathematical physics, and other fields. Connections to arithmetic combinatorics will be pursued.
Max ERC Funding
1 229 714 €
Duration
Start date: 2011-01-01, End date: 2016-12-31
Project acronym MANYBO
Project Many-body physics in gauge fields with ultracold Ytterbium atoms in optical lattices
Researcher (PI) Fabrice Gerbier
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Starting Grant (StG), PE2, ERC-2010-StG_20091028
Summary In this project, we will investigate the many-body physics of interacting ultracold atoms in presence of strong gauge fields. The practical implementation will use Ytterbium atoms in optical lattices. We will use two atoms in two internal states- the ground state and a long-lived excited state- trapped in suitably designed state-dependent lattice potentials. Coherent coupling between the two states will be used to ``write'' a spatially-dependent phase on the atomic wavefunction, which under suitable conditions will mimic the Aharonov-Bohm phase accumulated by charged particles moving in a gauge field. Using this technique, we will study the behavior of interacting bosonic and fermionic quantum gases in such artificial gauge potentials for different lattice geometries. We will look for strongly correlated states analogous to those observed for 2D electrons experiencing the fractional quantum Hall effect, and study the unusual behavior of their elementary excitations (``anyons''). These novel quantum phases will be primarily characterized using high-sensitivity imaging with single-site resolution, enabling spatially-resolved measurements of the spatial distribution and of its correlation functions. The project will first investigate the simpler case of an Abelian gauge potentials for bosons and fermions, then move to the more complex case of a non-Abelian $SU(2)$ gauge field using two-component fermions. The resulting system can be seen as a laboratory playground to study interacting quantum matter (bosonic or fermionic) coupled to well-defined gauge fields, a situation encountered in many domains of Physics, from high-energies to condensed matter.
Summary
In this project, we will investigate the many-body physics of interacting ultracold atoms in presence of strong gauge fields. The practical implementation will use Ytterbium atoms in optical lattices. We will use two atoms in two internal states- the ground state and a long-lived excited state- trapped in suitably designed state-dependent lattice potentials. Coherent coupling between the two states will be used to ``write'' a spatially-dependent phase on the atomic wavefunction, which under suitable conditions will mimic the Aharonov-Bohm phase accumulated by charged particles moving in a gauge field. Using this technique, we will study the behavior of interacting bosonic and fermionic quantum gases in such artificial gauge potentials for different lattice geometries. We will look for strongly correlated states analogous to those observed for 2D electrons experiencing the fractional quantum Hall effect, and study the unusual behavior of their elementary excitations (``anyons''). These novel quantum phases will be primarily characterized using high-sensitivity imaging with single-site resolution, enabling spatially-resolved measurements of the spatial distribution and of its correlation functions. The project will first investigate the simpler case of an Abelian gauge potentials for bosons and fermions, then move to the more complex case of a non-Abelian $SU(2)$ gauge field using two-component fermions. The resulting system can be seen as a laboratory playground to study interacting quantum matter (bosonic or fermionic) coupled to well-defined gauge fields, a situation encountered in many domains of Physics, from high-energies to condensed matter.
Max ERC Funding
1 099 913 €
Duration
Start date: 2010-11-01, End date: 2015-10-31
Project acronym MATHANA
Project Mathematical modeling of anaesthetic action
Researcher (PI) Axel Hutt
Host Institution (HI) INSTITUT NATIONAL DE RECHERCHE ENINFORMATIQUE ET AUTOMATIQUE
Call Details Starting Grant (StG), PE1, ERC-2010-StG_20091028
Summary General anaesthesia is an important method in today's hospital practice and especially in surgery. To supervise the depth of anaesthesia during surgery, the anaesthesist applies electroencephalography (EEG) and monitors the brain activity of the subject on the scalp. The applied monitoring machine calculates the change of the power spectrum of the brain signals to indicate the anaesthetic depth. This procedure is based on the finding that the concentration increase of the anaesthetic drug changes the EEG-power spectrum in a significant way. Although this procedure is applied world-wide, the underlying neural mechanism of the spectrum change is still unknown. The project aims to elucidate the underlying neural mechanism by a detailed investigating a mathematical model of neural populations.
The investigation is based on analytical calculations in a neural population model of the cortex involving intrinsic neural properties of brain areas and feedback loops to other areas, such as the loop between the cortex and the thalamus. Currently, there are two proposed mechanisms for the charactertisic change of the power spectrum: a highly nonlinear jump in the activation (so-called phase transition) and a linear behavior. The project mainly focusses on the nonlinear jump to finally rule it out or support it. A subsequent comparison to previous experimenta results aims to fit the physiological parameters. Since the cortex population is embedded into a network of other cortical areas and the thalamus, the corresponding analytical investigations takes into account external stochastic (from other brain areas) and time-periodic (thalamic) forces. To this end it is necessary to develop several novel nonlinear analysis technique of neural populations to derive the power spectrum close to the phase transition and conditions for physiological parameters.
Summary
General anaesthesia is an important method in today's hospital practice and especially in surgery. To supervise the depth of anaesthesia during surgery, the anaesthesist applies electroencephalography (EEG) and monitors the brain activity of the subject on the scalp. The applied monitoring machine calculates the change of the power spectrum of the brain signals to indicate the anaesthetic depth. This procedure is based on the finding that the concentration increase of the anaesthetic drug changes the EEG-power spectrum in a significant way. Although this procedure is applied world-wide, the underlying neural mechanism of the spectrum change is still unknown. The project aims to elucidate the underlying neural mechanism by a detailed investigating a mathematical model of neural populations.
The investigation is based on analytical calculations in a neural population model of the cortex involving intrinsic neural properties of brain areas and feedback loops to other areas, such as the loop between the cortex and the thalamus. Currently, there are two proposed mechanisms for the charactertisic change of the power spectrum: a highly nonlinear jump in the activation (so-called phase transition) and a linear behavior. The project mainly focusses on the nonlinear jump to finally rule it out or support it. A subsequent comparison to previous experimenta results aims to fit the physiological parameters. Since the cortex population is embedded into a network of other cortical areas and the thalamus, the corresponding analytical investigations takes into account external stochastic (from other brain areas) and time-periodic (thalamic) forces. To this end it is necessary to develop several novel nonlinear analysis technique of neural populations to derive the power spectrum close to the phase transition and conditions for physiological parameters.
Max ERC Funding
856 500 €
Duration
Start date: 2011-01-01, End date: 2015-10-31
Project acronym MINOS
Project Nuclear magic numbers off stability
Researcher (PI) Alexandre Obertelli
Host Institution (HI) COMMISSARIAT A L ENERGIE ATOMIQUE ET AUX ENERGIES ALTERNATIVES
Call Details Starting Grant (StG), PE2, ERC-2010-StG_20091028
Summary Atomic nuclei are finite systems composed of fermions, the nucleons, and essentially governed by the strong force and quantum mechanical laws. Their structure is characterized by single-particle orbitals grouped in energy shells, separated by energy gaps. The numbers of nucleons that correspond to fully filled shells are called magic and represent the backbone of nuclear structure. In this proposal, we propose a new approach to investigate the most neutron-rich systems ever reached and establish the shell structure in new regions of the nuclear chart where new magic numbers or strong shell reordering are expected or controversial. This will open new horizons in the terra incognita of the nuclear landscape. Beyond the fundamental question of the nuclear force, the assessment of new shell closures in the nuclear landscape is of primary importance to better understand the stellar nucleosynthesis in the Universe.
In-flight gamma spectroscopy of rare isotopes at intermediate energy is one of the most efficient tools to populate and measure excited states in exotic nuclei. We propose to develop a new method that will increase the sensitivity of prompt-gamma spectroscopy by more than one order of magnitude compared to existing setups. Experiments will be performed at the most competitive fragmentation radioactive-beam facilities worldwide. In the future, this program will take advantage of the European FAIR facility, Germany, coupled to the European new-generation gamma array AGATA spectrometer. When coupled to AGATA, the improvement will reach a factor of several hundreds. This new experimental technique will be strengthened by original developments in the theory of reaction mechanisms, which are also included in this proposal.
Summary
Atomic nuclei are finite systems composed of fermions, the nucleons, and essentially governed by the strong force and quantum mechanical laws. Their structure is characterized by single-particle orbitals grouped in energy shells, separated by energy gaps. The numbers of nucleons that correspond to fully filled shells are called magic and represent the backbone of nuclear structure. In this proposal, we propose a new approach to investigate the most neutron-rich systems ever reached and establish the shell structure in new regions of the nuclear chart where new magic numbers or strong shell reordering are expected or controversial. This will open new horizons in the terra incognita of the nuclear landscape. Beyond the fundamental question of the nuclear force, the assessment of new shell closures in the nuclear landscape is of primary importance to better understand the stellar nucleosynthesis in the Universe.
In-flight gamma spectroscopy of rare isotopes at intermediate energy is one of the most efficient tools to populate and measure excited states in exotic nuclei. We propose to develop a new method that will increase the sensitivity of prompt-gamma spectroscopy by more than one order of magnitude compared to existing setups. Experiments will be performed at the most competitive fragmentation radioactive-beam facilities worldwide. In the future, this program will take advantage of the European FAIR facility, Germany, coupled to the European new-generation gamma array AGATA spectrometer. When coupled to AGATA, the improvement will reach a factor of several hundreds. This new experimental technique will be strengthened by original developments in the theory of reaction mechanisms, which are also included in this proposal.
Max ERC Funding
1 121 520 €
Duration
Start date: 2010-11-01, End date: 2015-10-31
Project acronym MNIQS
Project Mathematics and Numerics of Infinite Quantum Systems
Researcher (PI) Mathieu Lewin
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Starting Grant (StG), PE1, ERC-2010-StG_20091028
Summary The purpose of the project is to study linear and nonlinear models arising in quantum mechanics and which are used to describe
matter at the microscopic and nanoscopic scales. The project focuses on physically-oriented questions (rigorous derivation of a
given model from first principles), analytic problems (existence and properties of bound states, study of solutions to timedependent
equations) and numerical issues (development of reliable algorithmic strategies). Most of the models are nonlinear and
describe physical systems possessing an infinite number of quantum particles, leading to specific difficulties.
The first part of the project is devoted to the study of relativistic atoms and molecules, while taking into account quantum
electrodynamics effects like the polarization of the vacuum. The models are all based on the Dirac operator.
The second part is focused on the study of quantum crystals. The goal is to develop new strategies for describing their behavior in
the presence of defects and local deformations. Both insulators, semiconductors and metals are considered (including graphene).
In the third part, attractive systems are considered (like stars or a few nucleons interacting via strong forces in a nucleus). The
project aims at rigorously understanding some of their specific properties, like Cooper pairing or the possible dynamical collapse of
massive gravitational objects.
Finally, the last part is devoted to general properties of infinite quantum systems, in particular the proof of the existence of the
thermodynamic limit
Summary
The purpose of the project is to study linear and nonlinear models arising in quantum mechanics and which are used to describe
matter at the microscopic and nanoscopic scales. The project focuses on physically-oriented questions (rigorous derivation of a
given model from first principles), analytic problems (existence and properties of bound states, study of solutions to timedependent
equations) and numerical issues (development of reliable algorithmic strategies). Most of the models are nonlinear and
describe physical systems possessing an infinite number of quantum particles, leading to specific difficulties.
The first part of the project is devoted to the study of relativistic atoms and molecules, while taking into account quantum
electrodynamics effects like the polarization of the vacuum. The models are all based on the Dirac operator.
The second part is focused on the study of quantum crystals. The goal is to develop new strategies for describing their behavior in
the presence of defects and local deformations. Both insulators, semiconductors and metals are considered (including graphene).
In the third part, attractive systems are considered (like stars or a few nucleons interacting via strong forces in a nucleus). The
project aims at rigorously understanding some of their specific properties, like Cooper pairing or the possible dynamical collapse of
massive gravitational objects.
Finally, the last part is devoted to general properties of infinite quantum systems, in particular the proof of the existence of the
thermodynamic limit
Max ERC Funding
905 700 €
Duration
Start date: 2010-10-01, End date: 2015-09-30
Project acronym MULTIMOD
Project Multi-Mathematics for Imaging and Optimal Design Under Uncertainty
Researcher (PI) Habib Ammari
Host Institution (HI) CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS
Call Details Advanced Grant (AdG), PE1, ERC-2010-AdG_20100224
Summary The aim of this interdisciplinary project is to develop new mathematical and statistical tools, probabilistic approaches, and inversion and optimal design methods to address emerging modalities in medical imaging, nondestructive testing, and environmental inverse problems. It merges the complementary expertise of the investigators in order to make a breakthrough in the field of
mathematical imaging and optimal design by solving the most challenging problems posed by new imaging modalities. The PI and Co-PI are leading experts in their respective fields (applied
analysis and probability) and their researches have very strong interdisciplinary nature.
The goal of this project is to synergize asymptotic imaging, stochastic modelling, and analysis of both deterministic and stochastic wave propagation phenomena. We want to throw a bridge across the deterministic and stochastic aspects and tools of mathematical imaging. This requires a deep understanding of the different scales in the physical problem, an accurate modelling of the noise sources, and fine mathematical analysis of complex phenomena. The emphasis of this project will be put on deriving for each of the challenging imaging problems that we will consider, the best possible imaging functionals in the sense of stability and resolution. For optimal design problems, we
will evaluate the effect of uncertainties on the geometrical or physical parameters and design accurate optimal design methodologies.
In this project, we will build an exceptional interdisciplinary research and an innovative approach to training in applied mathematics. We will train a new generation of applied mathematicians who will master both the probabilistic and analytical tools to best meet the challenges of emerging technologies.
Summary
The aim of this interdisciplinary project is to develop new mathematical and statistical tools, probabilistic approaches, and inversion and optimal design methods to address emerging modalities in medical imaging, nondestructive testing, and environmental inverse problems. It merges the complementary expertise of the investigators in order to make a breakthrough in the field of
mathematical imaging and optimal design by solving the most challenging problems posed by new imaging modalities. The PI and Co-PI are leading experts in their respective fields (applied
analysis and probability) and their researches have very strong interdisciplinary nature.
The goal of this project is to synergize asymptotic imaging, stochastic modelling, and analysis of both deterministic and stochastic wave propagation phenomena. We want to throw a bridge across the deterministic and stochastic aspects and tools of mathematical imaging. This requires a deep understanding of the different scales in the physical problem, an accurate modelling of the noise sources, and fine mathematical analysis of complex phenomena. The emphasis of this project will be put on deriving for each of the challenging imaging problems that we will consider, the best possible imaging functionals in the sense of stability and resolution. For optimal design problems, we
will evaluate the effect of uncertainties on the geometrical or physical parameters and design accurate optimal design methodologies.
In this project, we will build an exceptional interdisciplinary research and an innovative approach to training in applied mathematics. We will train a new generation of applied mathematicians who will master both the probabilistic and analytical tools to best meet the challenges of emerging technologies.
Max ERC Funding
1 920 000 €
Duration
Start date: 2011-04-01, End date: 2016-03-31
Project acronym OBSERVABLESTRING
Project The Low Energy Limit of String Theory and the Observable World
Researcher (PI) Mariana Grana
Host Institution (HI) COMMISSARIAT A L ENERGIE ATOMIQUE ET AUX ENERGIES ALTERNATIVES
Call Details Starting Grant (StG), PE2, ERC-2010-StG_20091028
Summary The long-standing challenge of string theory, confronting the real world, has become more pressing and at the same time tangible in view of the upcoming LHC. Since the low energy limit of the theory is the main stage where predictions can be compared with experimental data, the goal of this project is to develop a new unified framework to formulate, compute and analyze this limit and its phenomenology. Understanding the low energy limit of string theory at the level where it can be confronted with precision experiments requires two key elements. On one hand one must obtain the full low energy Lagrangians resulting from compactifications from ten to four dimensions. On the other hand, one must analyze the couplings of quarks and leptons, represented by open strings attached to branes. Attempts to construct four-dimensional effective theories have focused in the past on a particular class of six-dimensional spaces, but my work in the last few years has shown that realistic solutions arise from manifolds whose differential properties are actually much weaker and that these compactifications have an elegant reformulation in terms of a generalized version of Riemannian geometry. I plan to use the formalism of generalized geometry to obtain the full tree level, perturbative and non-perturbative corrections to the 4D LEEL resulting from compactifications on these manifolds, and to study their phenomenology. Obtaining the full LEEL is the key step towards understanding if the world as we see it today comes from a string theory compactification: only full knowledge of the Lagrangian allows us to determine in detail how these manifolds lead to theories having 4D isolated vacua with a tiny positive cosmological constant, and support branes whose gauge theory spectrum and couplings are those of the Standard Model. Furthermore, the LEEL will be compared with the data of tomorrow: masses and couplings of supersymmetric partners, if supersymmetry is found at the LHC.
Summary
The long-standing challenge of string theory, confronting the real world, has become more pressing and at the same time tangible in view of the upcoming LHC. Since the low energy limit of the theory is the main stage where predictions can be compared with experimental data, the goal of this project is to develop a new unified framework to formulate, compute and analyze this limit and its phenomenology. Understanding the low energy limit of string theory at the level where it can be confronted with precision experiments requires two key elements. On one hand one must obtain the full low energy Lagrangians resulting from compactifications from ten to four dimensions. On the other hand, one must analyze the couplings of quarks and leptons, represented by open strings attached to branes. Attempts to construct four-dimensional effective theories have focused in the past on a particular class of six-dimensional spaces, but my work in the last few years has shown that realistic solutions arise from manifolds whose differential properties are actually much weaker and that these compactifications have an elegant reformulation in terms of a generalized version of Riemannian geometry. I plan to use the formalism of generalized geometry to obtain the full tree level, perturbative and non-perturbative corrections to the 4D LEEL resulting from compactifications on these manifolds, and to study their phenomenology. Obtaining the full LEEL is the key step towards understanding if the world as we see it today comes from a string theory compactification: only full knowledge of the Lagrangian allows us to determine in detail how these manifolds lead to theories having 4D isolated vacua with a tiny positive cosmological constant, and support branes whose gauge theory spectrum and couplings are those of the Standard Model. Furthermore, the LEEL will be compared with the data of tomorrow: masses and couplings of supersymmetric partners, if supersymmetry is found at the LHC.
Max ERC Funding
945 000 €
Duration
Start date: 2011-02-01, End date: 2016-09-30
