相关论文: A lattice Poisson algebra for the Pohlmeyer reduct…

We generalize the initial steps of the Faddeev-Reshetikhin procedure to the AdS_5 x S^5 superstring theory. Specifically, we propose a modification of the Poisson bracket whose alleviated non-ultralocality enables to write down a lattice…

The Pohlmeyer reduced equations for strings moving only in the AdS subspace of AdS_5 x S^5 have been used recently in the study of classical Euclidean minimal surfaces for Wilson loops and some semiclassical three-point correlation…

We consider the Pohlmeyer-reduced formulation of the AdS_5 x S^5 superstring. It is constructed by introducing new variables which are algebraically related to supercoset current components so that the Virasoro conditions are automatically…

We consider the Pohlmeyer reduced sigma model describing AdS$_5$ minimal surfaces. We show that, similar to the affine Toda models, there exists a conformal extension to this model which admits a Lax formulation. The Lax connection is shown…

We consider non-ultra local linear Poisson algebras on a continuous line . Suitable combinations of representations of these algebras yield representations of novel generalized linear Poisson algebras or "boundary" extensions. They are…

As was observed by Grigoriev and Tseytlin, the Pohlmeyer-reduced AdS_2 x S^2 superstring theory possesses N=(2,2) worldsheet supersymmetry. We show, at the classical level, that the AdS_3 x S^3 and AdS_5 x S^5 superstring theories in the…

Poisson superalgebras are known as a $\mathbb{Z}_2$-graded vector space with two operations, an associative supercommutative multiplication and a super bracket tied up by the super Leibniz relation. We show that we can consider a single…

Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of the AdS_5 x S^5 superstring world-sheet theory in terms of physical degrees of freedom we construct the Pohlmeyer-reduced version of the corresponding sigma model.…

We classify nonultralocal Poisson brackets for 1-dimensional lattice systems and describe the corresponding regularizations of the Poisson bracket relations for the monodromy matrix . A nonultralocal quantum algebras on the lattices for…

Poisson superpair is a pair of Poisson superalgebra structures on a super commutative associative algebra, whose any linear combination is also a Poisson superalgebra structure. In this paper, we first construct certain linear and quadratic…

A new Lax representation for the Bogoyavlensky lattice is found, its $r$--matrix interpretation is elaborated. The $r$--matrix structure turns out to be related to a highly nonlocal quadratic Poisson structure on a direct sum of associative…

Using a Lax pair based on twisted affine $sl(2,R)$ Kac-Moody and Virasoro algebras, we deduce a r-matrix formulation of two dimensional reduced vacuum Einstein's equations. Whereas the fundamental Poisson brackets are non-ultralocal, they…

Using a Poisson bracket representation, in 3D, of the Lie algebra $\mathfrak{sl}(2)$, we first use highest weight representations to embed this into larger Lie algebras. These are then interpreted as symmetry and conformal symmetry algebras…

We consider integrability properties of the superstring on $AdS_{5}\times S^{5}$ background and construct a new one parameter family of currents which satisfies the vanishing curvature condition. We present the Hamiltonian analysis for the…

The link between (super)-affine Lie algebras as Poisson brackets structures and integrable hierarchies provides both a classification and a tool for obtaining superintegrable hierarchies. The lack of a fully systematic procedure for…

Using the Poisson current algebra of the supersymmetric principal chiral model, we develop the algebraic canonical structure of the model by evaluating the fundamental Poisson bracket of the Lax matrices that fits into the rs matrix…

We construct recursively an infinite number of Poisson structures for the supersymmetric integrable hierarchy governing the Pohlmeyer reduction of superstring sigma models on the target spaces AdS_{n}\times S^n, n=2,3,5. These Poisson…

With a motivation to find a 2-d Lorentz-invariant solution of the AdS_5 x S^5 superstring we continue the study of the Pohlmeyer-reduced form of this theory. The reduced theory is constructed from currents of the superstring sigma model and…

Using the notion of a contravariant derivative, we give some algebraic and geometric characterizations of Poisson algebras associated to the infinitesimal data of Poisson submanifolds. We show that such a class of Poisson algebras provides…

The nonlinear equations for the general nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type are derived and the integrability of these equations by the method of inverse scattering problem is proved. For these…