Modern Mathematical Physics:
Gravity, Supersymmetry and Strings
Leaders:  A.P. Isaev S.O. Krivonos A.S. Sorin 
Scientific leader:  A.T. Filippov 
Participating Countries and International organizations: Armenia, Australia, Brazil, Bulgaria, Canada, CERN, Czech Republic, Estonia, France, Germany, Greece, ICTP, India, Israel, Iran, Ireland, Italy, Japan,
Lithuania, Luxembourg, Norway, Poland, Portugal, Republic of Korea, Russia, Spain, Taiwan, Ukraine, United Kingdom, USA.
Issues addressed and main goals of research: 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 of 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 use 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 investigation and description of a variety
of classical and quantum integrable models and their exact solutions;
analysis of a wide range of problems in supersymmetric theories including models of superstrings and superbranes, study of nonperturbative regimes
in supersymmetric gauge theories;
development of cosmological models of the early Universe, primordial gravitational waves and black holes.
The decisive factor in solving the above problems will be the 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 the current year:
 Construction of renormalization group flows on curved manifolds via the holographic duality.
Studies of phase diagrams using the obtained holographic RG flows.
Calculation and study of thermal correlators corresponding to quantum KdV charges in 2d
CFT. Construction of the full KdV partition function in the case of free bosons.
Construction of holographic RG flows with several effective charges. Consideration of these
RG flows in terms of brane intersections in a relevant supergravity theory. Studies of the
RG flows in the
framework of the generalized SachdevYeKitaev model.
Development of a grouptheoretical approach for the twistor description of massless
particles with a continuous spin. The comparison of this approach with the Penrose twistor
program.
Construction of projectors for the irreducible representations of the multidimensional
Poincare group (for an arbitrary type of symmetry) based on the
results from the representation theory of the Brauer algebra and the methods of the Rmatrices
(the solutions of the YangBaxter equation, which are constructed in terms of the Brauer
algebra generators).
Study of the systems with partially broken supersymmetry, with an arbitrarily
high number of spontaneously broken supersymmetries, in particular,
systems of many N=1, d=3 scalar and vector multiplets, as well as their
analogues in higher dimensions.
Construction of nonsymmetric eigenfunctions of the deformed Macdonald–Ruijsenaars systems in terms of the
representation theory of the Ding–Iohara algebra and, in the explicit form, calculation of eigenvalues for these eigenfunctions.
Construction of quantum Lax pairs for the deformed Calogero–Moser systems (rational,
trigonometric, elliptic) by means of the Dunkl operators. Construction of symmetries of the elliptic Gaudin model by means
of the quantum spectral curve. Generalization of Manin matrices.
Construction of monotonic lagrangian tori of nonstandard type in toric and pseudotoric Fano manifolds in the framework of Mirror Symmetry.
Construction of examples of nonstandard
lagrangian tori which have nontrivial Maslov classes and, therefore, do not admit hamiltonian
deformations to the minimal ones.
Construction of the trigonometric and hyperbolic Calogero models with extended supersymmetry.
 Continuing the study of the quantum structure of N=(1,0), N=(1,1) and N=(2,0) supersymmetric gauge theories in 6 dimensions
by the harmonic superspace methods, constructing the superfield invariants and effective action of these theories, further revealing
of their relationships with the AdS/CFT correspondence. Analogous superfield analysis of N=(1,0) and N=(1,1) gauge theories with higherderivatives.
Study of the quantum superfield geometry of N=2, 5D super YangMills theory, finding out the relation of the relevant effective action with
the D4 brane action.
Investigations of multiparticle Calogerotype systems with extended Poincare and superconformal supersymmetries, construction of their
various SU(mn) deformations on the basis of the superfield gauging of matrix models. Construction of quantum versions of the hyperbolic
and trigonometric supersymmetric CalogeroSutherland models, analysis of their possible integrability. Building new mechanics models with
extended supersymmetry on curved spaces, analysis of their quantum properties, as well as the issues of their integrability and relationship
with the matrix models of string theory. Study of the question of possible uses of the models constructed in nuclear physics and highenergy particle physics.
Generalization, to the complex, quaternionic and projective spaces, of the known superintegrable oscillatorlike systems allowing the inclusion
of the constant magnetic/instanton external field, and further supersymmetrization of these generalized systems. Construction and study of the
superintegrable versions of the oscillator models with extra Calogerolike potentials on complex/quaternion projective spaces, in interaction
with the external constant magnetic/instanton fields, "weak" N=4 and N=8 supersymmetrization of such systems, finding out their superfield formulations.
Construction of hyperKahler and quaternionic analogs of the SmorodinskyWinternitz and Rosokhatius systems, as well as of their "weak" N=4 and N=8
supersymmetric extensions, analysis of their symmetries and finding their classical and quantummechanical solutions. Generalization to the
Calogerotype systems.
Construction of twistor formulations of particles and superparticles with a continuous spin (helicity), as well as their quantization in the component
and superfield approaches.
Further investigations of the properties of topological solitons in classical and quantum field theory in flat and curved spacetime. Analogous analysis
of the black hole solutions, as well as the localized fieldconfiguration solutions in various versions of the gravitation theory coupled to the matter
fields, including nonabelian gauge fields.
Analysis of the quasiclassical limits of the threepoint functions in the Liouville theory and its superextensions. Study of the light and heavy
asymptotic limits in these theories. Clearing up the properties of the fusion matrix based upon the analysis of these limits, as well as of the
relationship between the boundary threepoint function and the fusion matrix. Study of the boundary threepoint function in the heavy limit and its
computing proceeding from the boundary Liouville theory defined on the solutions with three boundary singularities. Exhibiting the information
about the monodromy of the solutions of the equations of Goin and Painleve VI by means of using the relationship of the conformal blocks with the
solutions of these equations in the heavy asymptotic limits.
 Study of algebrageometric structures related with the full symmetric Toda
system based on the representation theory, inverse scattering method and other modern methods of studying integrable systems. Explanation of the
full Toda system's integrability in terms of the Liealgebraic approach, search for the reason for the existence of large (commutative and noncommutative)
families of integrals of this system. Search for a general principle, behind the Bruhat order emerging in the phase portrait of this system,
as well as search for its analogs in the infinitedimensional limits of the system (the KdV system) and providing a complete description of the
integrands in the case of degenerate orbits of the Toda system, in particular on RP(n).
Study of stationary (black holes, black hole systems) and cosmological solutions (inflation, dark energy) in Einstein and modified gravitations
of the Horndeski type and others. Study of the prospects for the application of the Palatiny formalism, which is characterized by a smaller number
of singularities, in the construction of realistic cosmological models.
Investigation of a subclass of the Stephani models with ideal gas and a matterradiation mixture. Generalization of the model to the case with
nonzero cosmological constant and calculation of observable parameters. Calculation of the probability for a black hole formation in the early
universe at the dust stage from the growing density contrasts of the scalar inflaton field.
Investigation of the vacuum energy in the boundary vicinity for CFTs. Computation of the entanglement entropy and pursuing the relation between
the entropy and the geometry of the manifold and its boundary.
The aim of the forthcoming research is to obtain new constraints on the parameters of black holes and neutron stars from the observational data
acquired in 2019 by the Event Horizon Telescope and other observational facilities, as well as restrictions on the alternative theories of gravity.
Investigation of the cosmological perturbations in
covariant formulation of teleparallel gravity. Derivation of equations
for scalar perturbations within this approach and obtaining the spectrum of
scalar perturbations during inflation.
List of Activities   Activity or experiment  Leaders  
 Laboratory or other Division of JINR  Main researchers

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


BLTP
 M. Buresh, P. Fiziev, A.A. Golubtsova, N.Yu. Kozyrev, D.R. Petrosyan, M. Podoinitsyn, G.S. Pogosyan, A.V. Silantyev

2.  Supersymmetry  E.A. Ivanov 


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

3.  Quantum gravity, cosmology and strings  A.T. Filippov I.G. Pirozhenko V. Nesterenko 


BLTP
 B.M. Barbashov, I. Bormotova, E.A. Davydov, V.V. Nesterenko, A.B. Pestov, A.A. Provarov, G.I. Sharygin, E.A. Tagirov, P.V. Tretyakov,
P. Yaluvkova, A.F. Zakharov, 3 students


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

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



 Foundation ANSL


Australia
 Sydney
 Univ.


 Perth
 UWA


Brazil
 Sao Paulo, SP
 USP


 Juiz de Fora, MG
 UFJF


 Vitoria, ES
 UFES


Bulgaria
 Sofia
 INRNE BAS


Canada
 Edmonton
 U of A


 Montreal
 Concordia


CERN
 Geneva
 CERN


Czech Republic
 Opava
 SlU


 Prague
 CTU


 Rez
 NPI CAS


Estonia
 Tartu
 UT


France
 AnnecyleVieux
 LAPP


 Lyon
 ENS Lyon


 Marseille
 CPT


 Nantes
 SUBATECH


 Paris
 ENS



 LUTH


 Tours
 Univ.


Germany
 Bonn
 UniBonn


 Hannover
 LUH


 Leipzig
 UoC


 Oldenburg
 IPO


 Potsdam
 AEI


Greece
 Athens
 UoA


 Thessaloniki
 AUTH


ICTP
 Trieste
 ICTP


India
 Kolkata
 BNC



 IACS


 Chennai
 IMSc


Israel
 Tel Aviv
 TAU


Iran
 Tehran
 IPM


Ireland
 Dublin
 DIAS


Italy
 Trieste
 SISSA/ISAS


 Frascati
 INFN LNF


 Padua
 UniPd


 Pisa
 INFN


 Turin
 UniTo


Japan
 Tokyo
 UT



 Keio Univ.


Lithuania
 Vilnius
 VU


Luxembourg
 Luxembourg
 Univ.


Norway
 Trondheim
 NTNU


Poland
 Bialystok
 UwB


 Lodz
 UL


 Wroclaw
 UW


Portugal
 Aveiro
 UA


Republic of Korea
 Seoul
 SKKU


Russia
 Moscow
 ITEP



 LPI RAS



 MI RAS



 MSU



 SAI MSU


 Moscow, Troitsk
 INR RAS


 Chernogolovka
 LITP RAS


 Kazan
 KFU


 Novosibirsk
 NSU


 Protvino
 IHEP


 St. Petersburg
 PDMI RAS


 Tomsk
 TPU



 TSPU


Spain
 Bilbao
 UPV/EHU


 Santiago de Compostela
 USC


 Barcelona
 IEECCSIC


 Valencia
 IFIC


 Madrid
 ETSIAE


Taiwan
 Taoyuan City
 NCU


Ukraine
 Kiev
 BITP NASU


 Kharkov
 NSC KIPT



 KhNU


United Kingdom
 London
 Imperial College


 Cambridge
 Univ.


 Canterbury
 Univ.


 Durham
 Univ.


 Glasgow
 U of G


 Leeds
 UL


 Nottingham
 Univ.


USA
 Amherst, MA
 UMass


 Tempe, AZ
 ASU


 New York, NY
 CUNY



 SUNY


 College Park, MD
 UMD


 Coral Gables, FL
 UM


 Norman, OK
 OU


 Piscataway, NJ
 Rutgers


 Rochester, NY
 UR


