Participating Countries and International organizations:
Armenia, Australia, Brazil, Bulgaria, CERN, China, Czech Republic, France, Germany, Greece, Iran, Ireland, Israel, Italy, Japan, Kazakhstan, Kyrgyzstan, Poland, Portugal, Russia, Serbia, Spain, United Kingdom, USA.

The problem under study and the main purpose of the reserch:
The main task of the Theme is the development of mathematical methods for solving the most important problems of modern theoretical physics, namely: development of new mathematical methods for studying and describing a wide class of classical and quantum integrable systems and their exact solutions; analyzing and searching for solutions to a wide range of problems of supersymmetric theories, including models of strings and other extended objects; study of nonperturbative regimes in supersymmetric gauge theories; development of cosmological models of the early Universe, gravitational waves and black holes.

Brief annotation and scientific rationale:
Our project is devoted to important problems of modern mathematical physics. The three most important investigation directions of the project are the study of holographic duality, construction of supersymmetric theories and description of unitary irreducible representations of Poincare groups in higher dimensions. Each of these directions can be regarded separately but in our project we concentrate our attention on the problems which lie on the borders of these major directions. As byproducts, we study certain applied problems, including those that arise in connection with booster thematic.

Expected results upon completion of the project:
The first problem of the project is the study of algebraic and differential structures in holographical systems, which belongs to the subject of modern mathematical physics considered in the context of holographic duality. This part of the project is focused on the study of properties of integrable systems appearing in holographical models.

The second problem is devoted to the construction of an action of the non-Abelian N=(1,0), d=6 tensor multiplet possessing as many as possible numbers of properties of six dimensional superconformal theories. This problem is related to the first one since it is devoted to field theories with extended supersymmetry which are very important in the mathematical physics studies since they help to describe common properties of quantum fields theories and many aspects of the string theory.

The third problem of our project arises in the context of studies of the models with higher spin fields requiring a certain description of unitary irreducible representations of Poincare groups and symmetry groups of AdS spaces. According to Wigner, each irreducible representation of the four-dimensional Poincare group is assotiated with an elementary particle (field). This conception is generalized to the case of arbitrary dimension and to the case of other groups including supergroups. Therefore, when studying different field models, one first of all asks the question of classification and explicit construction of unitary irreducible representations of the symmetry group of the studied theory.

Expected results of the project in the current year: 
Calculation of color factors in infinite series of  Feynman diagrams arising in non-Abelian gauge theories based on the properties of the split Casimir operator. Search for new series of representations of all simple Lie algebras (not known within the framework of Vogel universality) that admit a universal description. In particular, search for universal formulas for all dimensions of these representations.

Construction and analysis of analytica  black hole solutions with AdS asymptotics in 3d N=(2,0) gauge supergravity coupled  to a sigma model with hyperbolic target space; study of the  thermodynamic properties of the constructed holographic RG flows at finite temperature.

Search for a formulation of pure N=(1,0), d=6 supergravity where anti-self-dual equation of motion of the tensor field is induced by a superfield version of the Pasti-Sorokin-Tonin mechanism.

Study of the continuous spin representation for the symmetry groups of the AdS and dS spaces. In particular, calculation of the Casimir operators of the corresponding algebra in dimension D=4 in a fairly general representation. Analysis of their spectrum within the framework of already proposed models for particles with continuous spin in spaces of constant curvature.

Brief annotation and scientific rationale:
The project is aimed at solving fundamental problems of modern theoretical physics associated with the development of superfield methods in gauge theories with extended supersymmetry in various dimensions, including extended supersymmetric mechanics. The implementation of the project includes the construction of new field and quantum-mechanical models with global and gauge symmetries, the development of new, including geometric, methods for studying the structure of these models at the classical and quantum levels, the study of the structure of the corresponding quantum effective actions and classical solutions of these models, including black holes. All tasks of the project are set by the modern development of theoretical physics and are organically joined by the unity of methods and approaches.

Expected results upon completion of the project:
Calculating all leading and subleading in the dimensional regularization parameter two-loop counterterms in 6D, N=(1,0) and N=(1,1) supersymmetric gauge theories.

Constructing a one-loop induced effective action in the theory of hypermultiplet interacting with N=2 supergravity in the harmonic superspace approach.

Development of the methods of calculation of the one-loop induced effective action in the theory of hypermultiplet coupled to external fields of N=2 harmonic gauge superfields.

Derivation of 4D, N=2 harmonic superfield formulation for N=2 supersymmetric gauge fermionic higher spin fields.

Working out 4D, N=2 superfield gauge theory of higher spin fields in the AdS space.

Development of effective methods for describing gauge fields and superfields of an infinite spin in an arbitrary space-time dimension.

Finding Lagrangians describing the interactions of infinite spin fields and higher spin fields with fields of a fixed spin.

Finding out superfield harmonic Lagrangians of sigma models obtained by T-duality from 2D, N=(4,4) supersymmetric hyperkahler and quaternion-kahler sigma models.

Building a superfield matrix formulation of new N=4 and N=8 supersymmetric extensions of integrable many-particle systems and their quantization.

Construction of new models of N-extended supersymmetric quantum mechanics by using the superfield  gauging  method, which describe the interaction of dynamic and semidynamic multiplets of various types.

Construction and study of N=4 models of supersymmetric mechanics based on the interaction of linear and nonlinear supermultiplets with the component content (4,4,0), (3,4,1) and (2,4,2).

Constructing the Hamiltonian formulation and performing quantization of the generalizations of systems with the nonlinear (2,4,2) supermultiplet.

Constructing an extension of N=4 supersymmetric mechanics with (3,4,1) supermultiplet to the class of systems parametrized by an arbitrary holomorphic function.

Construction and study of many-particle systems with nonlinear supermultiplets.

Construction of a superfield description of Calogero-type models with extended N≥4 supersymmetries.

Analysis of the integrability of N-extended supersymmetric systems of the Euler–Calogero–Moser and Calogero–Moser–Sutherland types for the A(n-1) series of the Coxeter group.

Finding an explicit form of the functionally independent conserved Liouville currents in N=2 supersymmetric Calogero models for all root systems of Coxeter groups.

Construction of two new exactly calculated rarefied elliptic beta integrals associated with special lens spaces and a special subgroup of the modular transformations group SL(2,Z).

Computation of a matrix of modular transformations of one-point conformal blocks on a torus in the Neveu-Schwarz sector of the N=1 superconformal Liouville field theory, based on the expression of this matrix as an integral of the product of certain elements of the fusion matrix.

Obtaining the difference equations for the fusion matrix in the Neveu-Schwarz sector of the N=1 superconformal Liouville field theory.
 

Finding a new class of solutions of GR with gauge multicomponent matter fields in models with spontaneous symmetry breaking.

Constructing and exploring a new class of solutions of extenged Einstein gravity with the Chern-Simons term that represents stationary rotating black holes.

Expected results of the project in the current year: 
Calculation of two-loop counterterms in 6D, N=(1,0) and N=(1,1) supersymmetric gauge theories, subleading in the dimensional regularization parameter.

Construction of the one-loop induced effective action in the hypermultiplet theory coupled to N=2 supergravity in the harmonic superspace approach.

Construction of the Lagrangian formulation for supersymmetric infinite spin field theory in external field of N=1 supergravity.

Construction of minimal interaction of infinite spin fields and higher spin fields with fixed spin fields.

Construction and study of the N=4 supersymmetric extension of the Pöschl-Teller model at the classical and quantum levels.

Construction of models of the N=4 supersymmetric mechanics with spin degrees of freedom based on the interaction of linear and nonlinear supermultiplets. Study of nonlinear multiplets as semi-dynamical (spin) multiplets.

Search for a superfield description of long reducible multiplets of the N=4 supersymmetric mechanics and building models with their interaction. Quantization of the constructed models.

Construction and study of the Hamiltonian formulation of relativistic particle systems with the Lagrangians depending on extrinsic curvatures of isotropic and non-isotropic curves in three- and four-dimensional Minkowski spaces.

Construction, based on the Olshanetsky-Perelomov method, of a set of Liouville currents and additional conserved charges for Calogero-Moser models with N=2 supersymmetry associated with root systems of groups of B_n, C_n and D_n series.

Study of the integrability of the Calogero-Moser-Sutherland models with N=2 and N=4 supersymmetry by finding the corresponding Lax pair and conserved currents. Construction of Lax pairs for the N-extended supersymmetric Euler-Calogero-Moser model.

Search for eigenfunctions of the two-particle Hamiltonian of the complex rational Ruijsenaars-Sutherland model.

Search for explicit construction of hairy black holes in the U(1) gauged Einstein-Skyrme-Maxwell theory and exploration of localized configurations representing multipolar pion stars stabilized by gravitational interaction.

Study of the Regge symmetry for 6j-symbols of unitary principal series representations of the SL(2,C) group. Study of the properties of 6j-symbols of unitary principal series representations of the SL(2,C) group in the large spin.

Brief annotation and scientific rationale:
The project is aimed at solving the fundamental problems of classical and quantum gravity and  conducting advanced theoretical research at the national and world level in this area at BLTP JINR. In classical gravity, the project is focused on studying all kinds of gravitational wave phenomena, including shock waves in General Relativity, as well as various sources of gravitational wave background such as cosmic strings. One of the directions of the project is the elaboration of cosmological models that explain the properties of the observable Universe based on field theory methods and modified gravity. In the field of quantum gravity, it is planned to develop an apparatus of quantum field theory in an external classical gravitational background and new methods for an approximate estimation of the effective gravitational action in various regimes. Asymptotic symmetries in gravity, the relationship between gravity, thermodynamics and quantum entanglement, the holographic properties of gravity, and the AdS/CFT correspondence will also be explored.

Expected results upon completion of the project:
Development of field theory methods against the background of shock gravitational waves using the method of supertranslations at the wave front; study of classical field effects induced by shock waves, including the astrophysical applications.

Study of classical effects in the gravitational field of shock gravitational waves, including the case of the gravitational field induced by null cosmic strings (cosmic strings moving at the speed of light); study of gravitational (electromagnetic) radiation induced by the motion of null cosmic strings near massive (charged) sources, estimation of the parameters of these objects corresponding to the observed characteristics of induced radiation.

Study of physical effects associated with the formation of caustics and other defects on the world sheet of the null cosmic string as possible sources of gravitational bursts; development of the holonomy method proposed for describing free classical fields against the background of a gravitational shock wave.

Quantization and study of quantum effects in the gravitational field of shock gravitational waves, calculation of the expectation value of the renormalized energy-momentum tensor.

Derivation and study of the properties of exact solutions of the Einstein equations related to the subject of this project, for example, the search for non-trivial solutions that have global hyperbolic isometry and allow the introduction of holonomy associated with these transformations.

Study of the gravitational entropy associated with various surfaces in Riemannian geometry, in particular, study of the entropy formed when the light cones of the past and future (causal diamonds) intersect, as well as study of quantum corrections and renormalization of this quantity.

Further development of spectral geometry methods applied to nonlinear spectral problems; using these methods to study the finite-temperature QFT on stationary manifolds of a general form, as well as the application of this theory to calculate the effects of quark-gluon matter taking into account rotation and acceleration.

Study of cosmological models of modified gravity, an attempt to explain on their basis the key characteristics of the observed cosmology such as the accelerated expansion of the Universe; the study of cosmological perturbations in a teleparallel theory with a non-minimal scalar-tensor coupling, where the main object is the torsion scalar, in contrast to general relativity, where the main object is the Ricci scalar.

Construction of integrable cosmological potentials for spatially flat cosmologies with one scalar field for searching and constructing realistic completely integrable inflationary models with a phase transition; study of phase transitions in quantum theory, including gravity, and the formation dynamics of walls separating regions with different field values, the development of the thick-wall approximation method taking into account gravity, as well as the construction and study of exactly solvable inflationary models with phase transitions.

Development of methods in the framework of the Picard-Lefschetz theory and their application for calculating Lorentz path integrals in problems of quantum field theory, gravity and cosmology, and, in particular, in problems of describing the lensing of gravitational waves.

Expected results of the project in the current year:
Study of dynamic compactification and obtaining the effective Higgs potential in multidimensional cosmological models with a scalar field and a Gauss-Bonet type term.

Study of the impact of plane shock gravitational waves on classical and quantum field systems. Consideration of shock gravitational waves from different sources (massless particle, null string, null brane), including shock gravitational waves with a time-dependent profile function.

Investigation of gravitational wave scattering by gravitating sources. Study of secondary shock waves in various field systems caused by primary shock gravitational waves.

Study of jumps in the energy-momentum  tensor of fields on null surfaces, their geometric interpretation in Einstein's theory of gravity. Comparison of non-analyticities of Lorentzian manifolds on null hypersurfaces (non-analyticity of curvature such as the delta function and theta function).

Study of the physical effects of flat shock gravitational  waves with a surface energy density distributed  along the wave front sourced by ultrarelativistic heavy ions (in the limiting case). Study of the effect of quantum particle production by shock gravitational  waves with a time-dependent profile function.

Collaboration