Related papers: T-Duality in 2-D Integrable Models
The aim of this work is focused on the investigation of the algebraic complete integrability of the Toda lattice associated with the twisted affine Lie algebra $a_4^{(2)}$. First, we prove that the generic fiber of the momentum map for this…
The most important examples of a double vector bundle are provided by iterated tangent and cotangent functors: TTM, TT^*M, T^*TM, and T^*T^*M. We introduce the notions of the dual double vector bundle and the dual double vector bundle…
We revisit sigma models on target spaces given by a principal torus fibration $X\to M$, and show how treating the 2-form B as a gerbe connection captures the gauging obstructions and the global constraints on the T-duality. We show that a…
We extend topological T-duality to the case of general circle bundles. In this setting we prove existence and uniqueness of T-duals. We then show that T-dual spaces have isomorphic twisted cohomology, twisted $K$-theory and Courant…
We prove that abelian Yang-Baxter deformations of superstring coset sigma models are equivalent to sequences of commuting TsT transformations, meaning T dualities and coordinate shifts. Our results extend also to fermionic deformations and…
Two-dimensional topological field theories possessing a non-abelian current symmetry are constructed. The topological conformal algebra of these models is analysed. It differs from the one obtained by twisting the $N=2$ superconformal…
Topological insulators and D-brane charges in string theory can both be classified by the same family of groups. In this paper, we extend this connection via a geometric transform, giving a novel duality of topological insulators which can…
Two dimensional gauged linear sigma models(GLSMs) with $(0,2)$ supersymmetry and $U(1)$ gauge group possesing global symmetries are considered. For the case obtained as a reduction from the $(2,2)$ supersymmetric GLSM, we find the Abelian…
Various examples of target space duality transformations are investigated up to two loop order in perturbation theory. Our results show that when using the tree level (`naive') transformation rules the dual theories are in general {\it…
We discuss the infinite dimensional algebras appearing in integrable perturbations of conformally invariant theories, with special emphasis in the structure of the consequent non-abelian infinite dimensional algebra generalizing $W_\infty$…
Within the framework of relative and absolute quantum field theories (QFTs), we present a general formalism for understanding polarizations of the intermediate defect group and constructing non-invertible duality defects in theories in $2k$…
Duality groups of Abelian gauge theories on four manifolds and their reduction to two dimensions are considered. The duality groups include elements that relate different space-times in addition to relating different gauge-coupling…
Full set of autonomous completely solvable differential systems of equations in total differentials is built by basis of infinitesimal operators, universal invariant, and structure constants of admited multiparametric Lie group (abelian and…
A set of two-dimensional semi-riemannian submanifolds of flat semi-riemannian manifolds is associated to each Toda theory. The method and an example are given to Toda theories associated to real finite dimensional Lie algebras.
The standard notion of the non-Abelian duality in string theory is generalized to the class of $\si$-models admitting `non-commutative conserved charges'. Such $\si$-models can be associated with every Lie bialgebra $(\cg ,\cgt)$ and they…
We show how the T-duality is realized for D-branes with noncommutative world-volume coordinates. We discuss D-branes wrapped on tori and the result is that the recently found noncommutative actions form a consistent collection due to the…
We collect evidence that the notion of path-ordered non-abelian integration admits an extension to two dimensions. We propose the corresponding notion of non-abelian 2-form along the lines of Lie algebroid theory and argue it is an…
We consider the relation between affine Toda field theories (ATFT) and Landau-Ginzburg Lagrangians as alternative descriptions of deformed 2d CFT. First, we show that the two concrete implementations of the deformation are consistent once…
These pedagogical lectures given at the Corfu Summer Institute 2018 review two generalised notions of T-duality, non-Abelian T-duality and Poisson-Lie duality, and their applications. We explain how each of these has seen recent application…
The non-Abelian two-dimensional Toda lattice and matrix sine-Gordon equations with self-consistent sources are established and solved. Two families of quasideterminant solutions are presented for the non-Abelian two-dimensional Toda lattice…