Related papers: Axial Vector Duality in Affine NA Toda Models
We discuss a relation between bicomplexes and integrable models, and consider corresponding noncommutative (Moyal) deformations. As an example, a noncommutative version of a Toda field theory is presented.
The non-abelian self-dual action in three dimensions is derived using the self-interaction mechanism.
The duality between a class of the Davey-Stewartson type coupled systems and a class of two-dimensional Toda type lattices is discussed. For the recently found integrable lattice the hierarchy of symmetries is described. Second and third…
We consider a U(1) Gauged Linear Sigma Model (GLSM) with (2,2) supersymmetry, leading to a susy vacua of the resolved conifold. It possesses the non-Abelian global symmetry SU(2)xSU(2). A non-Abelian T-duality can be constructed which can…
The solutions of a large class of hierarchies of zero-curvature equations that includes Toda and KdV type hierarchies are investigated. All these hierarchies are constructed from affine (twisted or untwisted) Kac-Moody algebras~$\ggg$.…
We review some of the progress in affine Toda field theories in recent years, explain why known dualities cannot easily be extended, and make some suggestions for what should be sought instead.
Supplementary comments about generalized Lie algebroids are presented and a new point of view over the construction of the Lie algebroid generalized tangent bundle of a (dual) vector bundle is introduced. Using the general theory of…
We introduce a notion of constructibility for \'etale sheaves with torsion coefficients over a suitable class of adic spaces. This notion is related to the classical notion of constructibility for schemes via the nearby cycles functor. We…
We give a gauge invariant formulation of $N=2$ supersymmetric abelian Toda field equations in \n2 superspace. Superconformal invariance is studied. The conserved currents are shown to be associated with Drinfeld-Sokolov type gauges. The…
The problem of quantum equivalence between non-linear sigma models related by Abelian or non-Abelian T-duality is studied in perturbation theory. Using the anomalous Ward identity for Weyl symmetry we derive a relation between the Weyl…
We study exhaustively the solution-generating transformations (dualities) that occur in the context of the low-energy effective action of superstring theory. We first consider target-space duality (``T duality'') transformations in absence…
We propose a general method for constructing boundary integrable Gaudin models associated with (twisted) affine algebras ${\cal G}^{(k)} (k=1, 2)$, where ${\cal G}$ is a simple Lie algebra or superalgebra. Many new integrable Gaudin models…
In this paper, we introduce the notion of derivations of Lie 2-algebras and construct the associated derivation Lie 3-algebra. We prove that isomorphism classes of non-abelian extensions of Lie 2-algebras are classified by equivalence…
The grading operators for all nonequivalent Z-gradations of classical Lie algebras are represented in the explicit block matrix form. The explicit form of the corresponding nonabelian Toda equations is given.
We show that every finite Abelian algebra A from congruence-permutable varieties admits a full duality. In the process, we prove that A also allows a strong duality, and that the duality may be induced by a dualizing structure of finite…
This is a short note on generalized $G_2$-structures obtained as a consequence of a $T$-dual construction given in a previous work of the authors together with Leonardo Soriani. Given classical $G_2$-structure on certain seven dimensional…
We describe a systematic way of the generalization, to models with non-linear duality, of the space-time covariant and duality-invariant formulation of duality-symmetric theories in which the covariance of the action is ensured by the…
Vertex operators are constructed providing representations of the exchange relations containing either the S-matrix of a real coupling (simply-laced) affine Toda field theory, or its minimal counterpart. One feature of the construction is…
The construction of a family of real Hamiltonian forms (RHF) for the special class of affine 1+1-dimensional Toda field theories (ATFT) is reported. Thus the method, proposed in [1] for systems with finite number of degrees of freedom is…
A relation between semi-direct sums of Lie algebras and integrable couplings of lattice equations is established, and a practicable way to construct integrable couplings is further proposed. An application of the resulting general theory to…