
 
  Status:  Approved for completion in 2018


Modern Mathematical Physics:
Strings and Gravity, Supersymmetry, Integrability
Leaders:  A.P. Isaev A.S. Sorin
S.O. Krivonos 
Scientific leader:  A.T. Filippov 
Participating Countries and International organizations: Australia, Austria, Armenia, Brazil, Bulgaria, Canada, CERN,
Czech Republic, France, Germany, Greece, Hungary, ICTP, India, Italy, Japan,
Norway, Poland, Romania, Russia, Serbia, Spain, Turkey, Ukraine, USA, United Kingdom.
Scientific Programme: The main purpose of research in modern mathematical physics is the development of mathematical methods for solving
the most important problems of modern theoretical physics: clarifying the nature of fundamental interactions and their
symmetries, construction and study of effective field models arising in the theory of strings and other extended objects,
uncovering the geometric description of quantum symmetries and their spontaneous breaking in the framework of search for a
unified theory of all fundamental interactions, including quantum gravity.
Mathematical physics in recent years has been characterized by increasing interest in identifying and effective used of
integrability in various areas, and in applying powerful mathematical methods of quantum groups, supersymmetry and noncommutative
geometry to quantum theories of fundamental interactions as well as to classical models.
The main goals and tasks of the research within the theme include:
development of new mathematical methods for description of a variety of integrable models and their exact classical and quantum solutions;
analysis of a wide range of problems in the theory of superstrings and superbranes, including study of nonperturbative regimes in supersymmetric
gauge theories; development of a microscopic description of black holes and constructing cosmological models of the early Universe.
The decisive factor to solve the above problems is a crucial use of the mathematical methods of the theory of integrable systems, quantum
groups and noncommutative geometry as well as superspace techniques.
Expected main results in 2018:
 Studies of topology and geometry of the moduli spaces of special Bohr — Sommerfeld lagrangian cycles in algebraic varieties.
Construction of canonical Berry bundles on the moduli spaces of special Bohr — Sommerfeld lagrangian cycles in algebraic varieties.
Construction of holographic renormalization group flows related to SL(2,C) Toda chains. Analysis of the obtained RG flows in the framework
of the gauge/gravity duality. Construction of solutions without a horizon (boson stars) with anti deSitter and anisotropic asymptotics.
Analysis of the solutions in the holographic framework.
Construction of KerrVaidya/ KerrNewmanVaidya solutions with AdS asymptotics for the D=5 supergravity model. Study of local operators (twopoint correlation functions)
for the constructed metrics via holography.
Application of the generalised Reshetikhin formula for the scalar products of the Bethe vectors to the problems of formfactor calculations of the local
operators in the quantum integrable models with high symmetry. Reduction of these quantities to the determinant forms and its application to the problem
of calculation of the correlation functions in the thermodynamic limits.
Construction of classical integrable systems on varieties of modules of the preprojective algebras and their applications to generalised KP
hierarchies. Construction of integrable deformed elliptic Calogero–Moser systems by means of the elliptic Dunkl operators. Construction of
eigenfunctions of the deformed Macdonald–Ruijsenaars systems by using the representation theory of the Ding–Iohara algebra.
Study of systems of oscillators, invariant with respect to deformations of Galilei algebra (which include most of noncompact simple
Lie algebras). Prove that for any of these algebras it is possible to make the equations of motion for a system of harmonic or PaisUhlenbeck
oscillators linear. Apply these results to particular algebras (including G_{2}).
Study the N=4 supersymmetric mechanics of many particles on curved spaces: generalize the necessary conditions for supersymmetry, including
the WDVV equations, find the condition for acceptable potentials, solve them in particular cases.
It is planned to obtain exact solutions for quantum problem of harmonic oscillator on twosheeted hyperboloid SO(3,1)/SO(3) in four coordinate
systems: spherical, polarcylindrical, equidistantcylindrical and equidistant, and to find the coefficients of interbasis expansion between given
coordinate systems. It is also planned to find a full solution for classical problems of KeplerCoulomb and harmonic oscillator on onesheeted
hyperboloid SO(3,1)/SO(2,1), by solving the HamiltonJacobi equations, and constructing the trajectories of motion.
Study of compact objects in modified theories of gravity.
Development of new methods for processing and analysis of observational data from detectors of gravitational waves.
Development of the theory and applications of Heun’s functions in problems of mathematical physics and theory of gravity.
 The twoloop quantum calculations in N=(1,1) 6D supersymmetric YangMills theory will be preformed in the harmonic superspace approach:
the question of UV divergences and finite contributions to the effective action will be elucidated. There will be constructed all independent invariants of
canonical dimension d=12 and the issue of their (as well as of higherdimensional invariants) possible application for constructing 6D BornInfeld theory
with the manifest N=(1,0) and hidden N=(1,1) 6D supersymmetries.
There will be constructed new SU(22) and SU(42) supersymmetric extensions of the CalogeroMoser type models as deformations of N=4 and
N=8 supersymmetric extensions, the issue of their integrability and relationships with the matrix models of string theory will be studied.
The study of 6D supergravity models in the offshell N = (1; 0) and onshell N = (1; 1) 6D harmonic superspaces will be started. The constraints of N = (1; 1) 6D
supergravity will be solved in terms of N = (1; 0) superfields.
Construction of superfield action for the manyparticle systems with N=4 and N=8 deformed supersymmetries. Superfield formulation of sigma model with WessZumino
term possessing the N=4 and N=8 deformed supersymmetries and describing the interaction of the spinning particle with an external gauge background.
Construction of models for spinning particles and superparticles using momentum twistors. Obtaining of transition amplitudes from the BFVBRST path integral.
Definition of geometries described by N=4 supersymmetric quantum mechanical sigma models with a variety of dynamical, semidynamical and gauge supermultiplets.
Determination of the type of supercharges for different geometries.
Construction of new hairy black holes linked to charged scalar clouds in the KerrNewman spacetime. Investigation of the near BPS spinning selfgravitating
Skyrmions. Construction of spinning black holes with the BPS Skyrme hair.
 It is planned to study various boundary effects (the Casimir effect for instance) in conformal theories, and their possible holographic duals in gravity
theories to comprehend the peculiarities of their strong coupling regime. To this end the Casimir energy will be derived in free conformal theories
with D=3,4,6 which obey the boundary conditions preserving conformal invariance at boundaries of various geometries. Specifically, in d=4 the calculation
will be performed for N=4 super YangMills theory. The results will be used to choose among different holographic descriptions those reproducing the Casimir
energy for conformal theories with boundaries.
Vacuum fluctuations of spinor and vector fields in the lattice background of ndimensional delta function potentials will be studied. Similar twodimensional
systems have attached recent attention related to the description of dispersion forces between polarizable sheets, for example graphene layers. The research
demands the development of differential operator’s selfajoint extensions, and spectral geometry, specifically, spectral zeta functions and heatkernel
expansions in singular background or with singular potential.
By making use of the twotime temperature Green functions, the vacuum friction force between macroscopic bodies will be calculated with account of all
orders in the relative velocity of the bodies.
We plan to perform the phase space analysis of some realistic f(R)gravity models. We also plan to calculate the cosmological perturbations in such kind of models.
Studying of scalartensor teleparallel gravity models and calculation of cosmological perturbations in such kind of models will be performed.
It is planned to study gravity model based on a nonlinear realization of affine and conformal groups. Study of the model’s quantum features and renormalization
properties in first and second perturbation theory order.
Study of Horndeski gravity model’s features.
Investigation of the massinflation phenomenon on Cauchy horizon of black holes depending on their electric and magnetic charges, angular momenta and presence
of hairs, both in Einstein gravity and in gravity theories with nonminimal coupling. Such investigation promotes our understanding of singularity issues in
solutions to gravity theories.
Investigation of the Horndeski models with Maxwell and YangMills fields applied to black holes and cosmologies. In cosmologies such theories attracted a lot
of interest because the corresponding lagrangian degenerates on de Sitter background. Recently we have shown that the presence of such quasiattractor gives
rise to natural finitetime inflation in Friedmann cosmology with SU(2) YangMills field. It is planned to continue our investigation of these models in
the firstorder (EinsteinPalatini) formalism, when connection is treated as an independent variable. For a theories with nonminimal coupling of matter
to gravity there is no a priori reason considering the metriccompatible connection, which leads to diverse dynamical models with new solutions.
Exact Stephani solutions with variable spatial curvature will be studied, their possible impact on inflationary cosmology and general topological properties
will be investigated. Question of cosmological horizon in the EinsteinStraus vacuole model and LemaitreTolmanBondi model will be studied.
Prospects for the formation of structures in the inhomogeneous models will be examined, observable cosmological parameters will be evaluated and experimental
data will be fitted. The Stephani and CDM cosmological models will be compared from the phenomenological point of view.
Mannheim's conformal gravity will be analyzed, galactic rotation curves without presence of dark matter in light of uptodate cosmological measurements will
be obtained. Internal structure of the Mannheim's theory, problems with unitarity, and its critical evaluation as a possible candidate for quantum gravity will be analyzed.
List of Activities   Activity or experiment  Leaders  
 Laboratory or other Division of JINR  Main researchers

1.  Quantum groups and integrable systems  A.P. Isaev 


BLTP
 P. Fiziev, J. Fuksa, A.A. Golubtsova, S.O. Krivonos, N.Yu. Kozyrev, V.K. Mitrjushkin, D.R. Petrosyan, G.S. Pogosyan,
A.V. Silantyev, N.A. Tyurin + 1 student

2.  Supersymmetry  E.A. Ivanov 


BLTP
 S.A. Fedoruk, M. Pientek, A. Pietrikovsky, I.B. Samsonov, S.S. Sidorov, Ya.M. Shnir,
A.O.Sutulin

3.  Quantum gravity, cosmology and strings  A.T. Filippov V.V. Nesterenko A.S. Sorin 


BLTP
 B.M. Barbashov, I. Bormotova, E.A. Davydov, B.N. Latosh, A.B. Pestov, I.G. Pirozhenko,
E.A. Tagirov, P.V. Tretyakov, P. Yaluvkova + 3 students


LIT
 I.L. Bogoliubsky, A.M. Chervyakov

Collaboration 
Country or International Organization  City  Institute or Laboratory 
Armenia
 Yerevan
 YSU


Australia
 Sydney
 Univ.


 Perth
 UWA


Austria
 Vienna
 TU Wien


Brazil
 Sao Paulo, SP
 USP


 Juiz de Fora, MG
 UFJF


Bulgaria
 Sofia
 INRNE BAS



 SU


Canada
 Montreal
 McGill



 UdeM


 Edmonton
 U of A


 Vancouver
 TRIUMF


CERN
 Geneva
 CERN


Czech Republic
 Opava
 SlU


 Prague
 CTU



 CU


 Rez
 NPI ASCR


France
 AnnecyleVieux
 LAPP


 Dijon
 UB



 IMB


 Lyon
 ENS Lyon


 Marseille
 CPT


 Nantes
 SUBATECH


 Paris
 ENS



 LUTH



 LPTHE


 Palaiseau
 Polytech


 Valenciennes
 UVHC


Germany
 Berlin
 FU Berlin



 MBI


 Bielefeld
 Univ.


 Bonn
 UniBonn


 Dortmund
 TU Dortmund


 Hannover
 LUH


 Jena
 Univ.


 Leipzig
 UoC


 Munich
 MPIP


 Oldenburg
 IPO


 Potsdam
 AEI


Greece
 Athens
 UoA


Hungary
 Budapest
 Wigner RCP


ICTP
 Trieste
 ICTP


India
 Calcutta
 BNC



 IACS


 Chennai
 IMSc


Italy
 Bari
 INFN


 Frascati
 INFN LNF


 Naples
 INFN


 Padua
 UniPd


 Pavia
 INFN


 Pisa
 INFN


 Salerno
 UNISA


 Trieste
 SISSA/ISAS


 Turin
 UniTo


Japan
 Fukuoka
 Kyushu Univ.


 Kyoto
 KSU



 RIMS



 YITP


 Tsukuba
 KEK


 Fukusima
 Fukusima Univ.


 Tokyo
 UT


Luxembourg
 Luxembourg
 Univ.


Norway
 Trondheim
 NTNU


Poland
 Warsaw
 NCAC PAS



 UW


 Krakow
 JU



 NINP PAS


 Lodz
 UL


 Wroclaw
 UW


Romania
 Bucharest
 IFINHH


Russia
 Moscow
 ITEP



 LPI RAS



 MSU



 MI RAS



 NRU HSE



 VNIIMS



 PFUR



 SAI MSU


 Moscow, Troitsk
 INR RAS


 Chernogolovka
 LITP RAS


 Dolgoprudny
 MIPT


 Kazan
 KFU


 Novosibirsk
 NSU


 Protvino
 IHEP


 St. Petersburg
 PDMI RAS



 SPbSU


 Tomsk
 TPU



 TSPU


Serbia
 Belgrade
 IPB



 Univ.


Spain
 Bilbao
 UPV/EHU


 Barcelona
 IEECCSIC


 Valencia
 IFIC


 Madrid
 ETSIAE


Turkey
 Istanbul
 BU


 Izmir
 IZTECH


Ukraine
 Kiev
 BITP NASU


 Kharkov
 NSC KIPT


United Kingdom
 London
 Imperial College


 Cambridge
 Univ.


 Durham
 Univ.


 Liverpool
 Univ.


 Southampton
 Univ.


 York
 Univ.


 Glasgow
 U of G


 Leeds
 UL


 Brighton
 US


USA
 New York, NY
 CUNY



 RU



 SUNY


 Cincinnati, OH
 UC


 College Park, MD
 UMD


 Coral Gables, FL
 UM


 Minneapolis, MN
 U of M


 Norman, OK
 OU


 Philadelphia, PA
 Penn


 Piscataway, NJ
 Rutgers


 Rochester, NY
 UR


