Related papers: Integrable Zhaidary equations: reductions and gaug…
Integrable models of 1+1 dimensional gravity coupled to scalar and vector fields are briefly reviewed. A new class of integrable models with nonminimal coupling to scalar fields is constructed and discussed.
In the first part of the thesis, and after an introduction to certain models of modified gravity, we study consistent Lagrangians for Lorentz invariant (massive and massless) spin-2 and spin-3/2 particles in flat space. The second part of…
Appropriate restrictions of Lax operators which allows to construction of (2+1)-dimensional integrable field systems, coming from centrally extended algebra of pseudo-differential operators, are reviewed. The gauge transformation and the…
Integrable systems of the sine-Gordon/Liouville type, which arise from reducing the BPS equations for solutions invariant under 16 supersymmetries in Type IIB supergravity and M-theory, are shown to be special cases of an infinite family of…
We describe the results that have so far been obtained in the classification problem for integrable (2+1)-dimensional systems of hydrodynamic type. The systems of Gibbons--Tsarev type are the most fundamental here. A whole class of…
We develop a systematic approach to compute the subsystem trace distances and relative entropies for subsystem reduced density matrices associated to excited states in different symmetry sectors of a 1+1 dimensional conformal field theory…
We investigate integrable second order equations of the form F(u_{xx}, u_{xy}, u_{yy}, u_{xt}, u_{yt}, u_{tt})=0. Familiar examples include the Boyer-Finley equation, the potential form of the dispersionless Kadomtsev-Petviashvili equation,…
We consider the close relation between duality in N=2 SUSY gauge theories and integrable models. Various integrable models ranging from Toda lattices, Calogero models, spinning tops, and spin chains are related to the quantum moduli space…
This is a comprehensive study of the relations between the global, local and pointwise variants of irreducibility and integrity of schemes, including examples and counterexamples, and aimed especially at learners of algebraic geometry.
For the Davey-Stewartson I equation, which is an integrable equation in 1+2 dimensions, we have already found its Lax pair in 1+1 dimensional form by nonlinear constraints. This paper deals with the second nonlinearization of this 1+1…
We present higher-spin algebras containing a Poincar\'e subalgebra and with the same set of generators as the Lie algebras that are relevant to Vasiliev's equations in any space-time dimension $D \geq 3$. Given these properties, they can be…
Integrability of the (2+1)-dimensional Gauss-Codazzi-Mainardi equation is considered. It is shown that this equation is the particular cases of the Yang-Mills-Higgs-Bogomolny and self-dual Yang-Mills equations.
General spin-1/2 chains with symmetric nearest-neighbor interaction are studied. We rigorously prove that all spin models in this class, except for known integrable systems, are non-integrable in the sense that they possess no nontrivial…
A systematic study of the discrete second order projective system is presented, complemented by the integrability analysis of the associated multilinear mapping. Moreover, we show how we can obtain third order integrable equations as the…
BGG-equations are geometric overdetermined systems of PDEs on parabolic geometries. Normal solutions of BGG-equations are particularly interesting and we give a simple formula for the necessary and sufficient additional integrability…
This is an elementary introduction to basic tools of supersymmetry: the spacetime symmetries, gauge theory and its application in gravity, spinors and superalgebras. Special attention is devoted to conformal and anti-de Sitter algebras.
We generalize the exact field theoretic correspondence proposed in arXiv:1103.5726 and embed it into the context of refined topological string. The correspondence originally proposed from the common integrable structures in different field…
Using a recently developed method, based on a generalization of the zero curvature representation of Zakharov and Shabat, we study the integrability structure in the Abelian Higgs model. It is shown that the model contains integrable…
We describe a class of integrable models of 1+1 and 1-dimensional dilaton gravity coupled to scalar fields. The models can be derived from high dimensional supergravity theories by dimensional reductions. The equations of motion of these…
The exact solutions to quantum string and gauge field theories are discussed and their formulation in the framework of integrable systems is presented. In particular I consider in detail several examples of appearence of solutions to the…