Final Report Summary - GAUGE-STRING DUALITY (GAUGE-STRING DUALITY AND NON-EQUILIBRIUM PHYSICS)
Gauge-string duality or holography is a theoretical framework allowing one to explore properties of certain strongly interacting quantum systems inaccessible for study by other known methods. The project focused on investigating equilibrium and non-equilibrium states of such systems. Understanding the non-equilibrium regime of strongly coupled quantum theories is of interest for experimental programs involving heavy ion collisions at Large Hadron Collider and Relativistic Heavy Ion Collider, condensed matter physics of cold atoms and high-temperature superconductors, and for other applications. During the four years of the active phase of the project, the research group has obtained the following results:
Thermalization process in strongly interacting quantum systems: The existing analysis of thermalization involving the quantity known as the entanglement entropy was generalized to theories which do not exhibit conformal or Lorentz symmetry. The sensitivity of the thermalization description in gauge-string duality to the specific model of thermalization was investigated. It was found that the late-time dynamics is universal while the early-time dynamics is not. New methods of computing two-point correlation functions in holographic thermalization scenarios were developed, it was shown that the two existing prescriptions are identical.
Holographic approach to turbulence: Understanding turbulence remains a major challenge for physics. Exploring the holographic mapping between fluids and black holes, a novel analytical formula for the turbulent structure function exponents satisfying all theoretical constraints and showing excellent agreement with existing experimental and numerical data has been proposed.
Gauge-string duality and condensed matter physics: New models of lattices and quantum impurities in strongly coupled media were built and explored, including the two-impurity Kondo model and the Mott insulator model. Extensions of holographic techniques to describe non-relativistic systems were obtained. Derivation of the "first law of the entanglement rates" by members of the group became an important step in understanding the entanglement entropy and its uses in quantum theory.
Gauge-string duality and heavy ion physics: Methods of “tomography” of the strongly coupled quark-gluon plasma are being developed using the dual string theory description. The existing equilibration and energy loss mechanisms have been generalized to plasmas with non-vanishing baryon chemical potential. It was shown that the behavior of finite-temperature quantum field theories at large but finite coupling is qualitatively different in some aspects from their behavior at the infinitely large coupling. The difference is consistent with the expectations summarizing the experience of perturbative calculations (e.g. in kinetic theory). It is also consistent with the picture of "unreasonable effectiveness" of hydrodynamics (i.e. validity of hydrodynamic description beyond the formal applicability range, for example, in the absence of local isotropy), evidence for which has been emerging in recent years from various studies. It was shown by the group that hydrodynamic description at strong coupling has a wider applicability range than at weak coupling. This is consistent with the picture emerging from LHC-RHIC experimental results. The equilibrium and off-equilibrium behavior of gauge theories at finite baryon density (and finite temperature) have been investigated for a number of potential physical observables. These methods are useful for future colliders such as NICA investigating the vicinity of the conjectured critical point in QCD.
Gauge-string duality and fluid dynamics at strong coupling: Coupling constant corrections to known expressions for the transport coefficients of strongly interacting quantum fluid have been computed. It was found that the universal relation between second-order coefficients holds also to next to leading order in all instances checked.
The research results were summarized in 38 papers, 5 preprints, and 4 dissertations. The group organized three high-profile workshops in Oxford in 2016-2017, attended by 89 researchers from around the world. The group has established an independent Holography seminar series in Oxford (2013 – 2017), with 86 two-hour-long seminars given by researchers from the UK and overseas. The group hosted 93 visitors in 2013-2017.
Thermalization process in strongly interacting quantum systems: The existing analysis of thermalization involving the quantity known as the entanglement entropy was generalized to theories which do not exhibit conformal or Lorentz symmetry. The sensitivity of the thermalization description in gauge-string duality to the specific model of thermalization was investigated. It was found that the late-time dynamics is universal while the early-time dynamics is not. New methods of computing two-point correlation functions in holographic thermalization scenarios were developed, it was shown that the two existing prescriptions are identical.
Holographic approach to turbulence: Understanding turbulence remains a major challenge for physics. Exploring the holographic mapping between fluids and black holes, a novel analytical formula for the turbulent structure function exponents satisfying all theoretical constraints and showing excellent agreement with existing experimental and numerical data has been proposed.
Gauge-string duality and condensed matter physics: New models of lattices and quantum impurities in strongly coupled media were built and explored, including the two-impurity Kondo model and the Mott insulator model. Extensions of holographic techniques to describe non-relativistic systems were obtained. Derivation of the "first law of the entanglement rates" by members of the group became an important step in understanding the entanglement entropy and its uses in quantum theory.
Gauge-string duality and heavy ion physics: Methods of “tomography” of the strongly coupled quark-gluon plasma are being developed using the dual string theory description. The existing equilibration and energy loss mechanisms have been generalized to plasmas with non-vanishing baryon chemical potential. It was shown that the behavior of finite-temperature quantum field theories at large but finite coupling is qualitatively different in some aspects from their behavior at the infinitely large coupling. The difference is consistent with the expectations summarizing the experience of perturbative calculations (e.g. in kinetic theory). It is also consistent with the picture of "unreasonable effectiveness" of hydrodynamics (i.e. validity of hydrodynamic description beyond the formal applicability range, for example, in the absence of local isotropy), evidence for which has been emerging in recent years from various studies. It was shown by the group that hydrodynamic description at strong coupling has a wider applicability range than at weak coupling. This is consistent with the picture emerging from LHC-RHIC experimental results. The equilibrium and off-equilibrium behavior of gauge theories at finite baryon density (and finite temperature) have been investigated for a number of potential physical observables. These methods are useful for future colliders such as NICA investigating the vicinity of the conjectured critical point in QCD.
Gauge-string duality and fluid dynamics at strong coupling: Coupling constant corrections to known expressions for the transport coefficients of strongly interacting quantum fluid have been computed. It was found that the universal relation between second-order coefficients holds also to next to leading order in all instances checked.
The research results were summarized in 38 papers, 5 preprints, and 4 dissertations. The group organized three high-profile workshops in Oxford in 2016-2017, attended by 89 researchers from around the world. The group has established an independent Holography seminar series in Oxford (2013 – 2017), with 86 two-hour-long seminars given by researchers from the UK and overseas. The group hosted 93 visitors in 2013-2017.