Modern Mathematical Physics:
Strings and Gravity, Supersymmetry, Integrability
Leaders:  A.P. Isaev A.S. Sorin 
Deputy:  S.O. Krivonos 
Scientific leader:  A.T. Filippov 
Participating Countries and International Organizations: Australia, Austria, Armenia, Belarus, Brazil, Bulgaria, Canada, CERN,
Czech Republic, France, Germany, Greece, Hungary, ICTP, India, Italy, Japan,
Norway, Poland, Romania, Russia, Serbia, Spain, Turkey, Ukraine, United Kingdom, USA.
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 2017:
 Construction of supergravity backgrounds which describe intersecting D(M)brane solutions with Lifshitzlike asymptotics. Analysis
of the obtained solutions in the framework of the gauge/gravity duality.
Investigation of correlation functions between a Wilson loop and local photons in the obtained backgrounds using the holographic approach.
Construction and analysis of solutions without a horizon (boson stars) with Lifshitzlike asymptotics. Construction of KerrVaidya/ KerrNewmanVaidya
solutions with AdS asymptotics for D=5 supergravity model.
Study of local operators (twopoint correlation functions) for the constructed metrics via holography.
Study of systems with onehalf spontaneously broken supersymmetry and construction of the component action for the BornInfeld theory with N=4,
d=4 supersymmetry, with N=2 vector multiplet as Goldstone superfield.
Construction of the supersymmetric extentions of the mechanics, including the PaisUhlenbeck oscillator with specific frequencies, which are
invariant with respect to the lconformal Galilei group or its deformations.
Calculation of the monodromy matrix elements action onto universal Bethe vectors in the quantum integrable models associated with supersymmetric extension
of the Yangian double. Application of these formulas for obtaining a supersymmetric analog of the Reshetikhin's formula for the scalar products of the Bethe
vectors in the supersymmetric models.
Study of the universal Bethe vectors for the quantum integrable models associated with gl(4) and gl(2,2) spin chains. Study of the representations
of connected Yangians with the aim to obtain the correlation functions in quantum integrable models.
In the framework of special BohrSommerfeld geometry, applications to the case when the phase space is not simply connected will be studied.
Investigation of a relation between special BohrSommerfeld geometry and the Hitchin integrable systems in the simplest case of riemannian surfaces of genus > 1.
Construction of moduli spaces of special BohrSommerfeld cycles in the algebraic case. It will be shown that in the algebraic case these moduli spaces are finite dimensional.
 The N = (1; 1); 6D SYM superfield invariants including the candidate counterterms found earlier from the pure symmetry considerations will
be reproduced from the fullfledged quantum perturbation theory in N = (1; 1) and N = (1; 0) harmonic superspaces. The background field
method for N = (1; 1); 6D SYM theory will be developed in full generality.
Construction and study of the SU(21) and SU(22) invariant extensions of the CalogeroMoser models as deformations of N = 4 supersymmetric extensions.
The models of N = 4 supersymmetric quantum mechanics with "long multiplets", as well as their SU(21) deformations, will be thoroughly studied,
their bosonic target geometry will be revealed and quantum spectrum will be found for a few particular cases.
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 deformed supersymmetry. Superfield formulation of sigma model with WessZumino
term possessing the N=4 deformed supersymmetry 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.
 Observations of bright stars near the Galactic Center will be used for obtaining constraints on modification of the Newton gravity law in
the weak field approximation. The bounds on a graviton mass will be obtained also proceeding from a potential reconstruction at the Galactic Center.
Realistic inflation scenarios consistent with observational data from Plank2015 will be developed by making use of the classical YangMills fields
nonminimally coupled to gravity.
Description of the scalartensor perturbations in modified theories of gravity without the Einstein frame; in particular, in theories with an arbitrary
function of the torsion scalar.
The stability of modified gravity theories with higher derivatives will be studied regarding different perturbations.
The explicit compact formulae are expected to be derived for the forces exerted on the material medium by the electromagnetic field, taking advantage
of the different forms for the relevant energymomentum tensor.
Derivation of the vacuum energy of quantized fields in the presence of crossed cosmic strings and extraction of its finite part depending on the strings' mutual position.
Study of the vacuum fluctuations on the lattice background formed by multidimensional delta functions.
Construction of integrable scalar cosmologies with a cubic integral of motion.
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
 S.A. Belev, A.A. Golubtsova, I. Bormotova, S.O. Krivonos, N.Yu. Kozyrev, R.M. MirKasimov, S.Z. Pakulyak, G.S. Pogosyan,
N.A. Tyurin, + 4 students

2.  Supersymmetry  E.A. Ivanov 


BLTP
 S.A. Fedoruk, M. Pientek, S.S. Sidorov, Ya.M. Shnir,
A.Pietrikovsky, A.Rivasplata, A.O. Sutulin, + 2 students

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


BLTP
 B.M. Barbashov, E.A. Davydov, D.V. Fursaev, A.B. Pestov, I.G. Pirozhenko,
A.D. Popov, E.A. Tagirov, P.V. Tretyakov, + 3 students


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

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


Australia
 Sydney
 Univ.


 Crawley
 UWA


Austria
 Vienna
 TU Wien


Belarus
 Minsk
 IP NASB



 BSU


Brazil
 Sao Paulo, SP
 USP


 Juiz de Fora, MG
 UFJF


Bulgaria
 Sofia
 INRNE BAS



 SU


Canada
 Montreal
 McGill



 UdeM


 Edmonton
 U of A


CERN
 Geneva
 CERN


Czech Republic
 Opava
 SlU


 Prague
 CTU



 CU


 Rez
 NPI ASCR


France
 AnnecyleVieux
 LAPP



 LAPTh


 Dijon
 UB


 Lyon
 ENS Lyon


 Marseille
 CPT


 Nantes
 SUBATECH


 Paris
 ENS



 LUTH



 LPTHE


 Palaiseau
 Polytech


 Valenciennes
 UVHC


Germany
 Berlin
 FU Berlin



 HUB



 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


India
 Calcutta
 BNC


Italy
 Bari
 INFN


 Frascati
 INFN LNF


 Naples
 INFN


 Padua
 UniPd


 Pavia
 INFN


 Pisa
 INFN


 Salerno
 UNISA


 Trieste
 SISSA/ISAS


 Turin
 INFN


ICTP
 Trieste
 ICTP


Japan
 Fukuoka
 Kyushu Univ.


 Kyoto
 KSU



 RIMS



 YITP


 Tsukuba
 KEK


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


 Moscow, Troitsk
 INR RAS


 Chernogolovka
 LITP RAS


 Protvino
 IHEP


 St. Petersburg
 PDMI RAS



 SPbSU


 Tomsk
 TPU


Serbia
 Belgrade
 IPB



 Univ.


Spain
 Bilbao
 UPV/EHU


 Barcelona
 IEECCSIC


 Valencia
 IFIC


Turkey
 Istanbul
 BU


 Izmir
 IZTECH


USA
 New York, NY
 CUNY



 RU



 SUNY


 Baltimore, MD
 JHU


 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


Ukraine
 Kiev
 BITP NASU


 Kharkov
 KFTI


United Kingdom
 London
 Imperial College


 Cambridge
 Univ.


 Durham
 Univ.


 Liverpool
 Univ.


 Southampton
 Univ.


 York
 Univ.


