Related papers: T-Duality for Coset Models

A discrete version of Lagrangian reduction is developed in the context of discrete time Lagrangian systems on $G\times G$, where $G$ is a Lie group. We consider the case when the Lagrange function is invariant with respect to the action of…

We define generalized dualities for heterotic and type I strings based on consistent truncations to half-maximal gauged supergravities in more than three dimensions. The latter are constructed from a generalized Scherk-Schwarz ansatz in…

This is a study of induced nonlinear realizations of a Lie group G in which the presence of one field induces nonlinear transformations on another field. The covariant derivative structure is similar in form to that for local gauge theory.…

The Langlands Program was launched in the late 60s with the goal of relating Galois representations and automorphic forms. In recent years a geometric version has been developed which leads to a mysterious duality between certain categories…

We apply the framework developed in Target Space Duality I: General Theory. We show that both nonabelian duality and Poisson-Lie duality are examples of the general theory. We propose how the formalism leads to a systematic study of duality…

In a recent publication a procedure was developed which can be used to derive completely gauge invariant models from general Lagrangian densities with $N$ order of derivatives and $M$ rank of tensor potential. This procedure was then used…

We generalize the $(n+1)$-dimensional twisted $R$-Poisson topological sigma model with flux on a target Poisson manifold to a Lie algebroid. Analyzing consistency of constraints in the Hamiltonian formalism and the gauge symmetry in the…

After reviewing some of the fundamental aspects of Drinfel'd doubles and Poisson-Lie T-duality, we describe the three-dimensional isotropic rigid rotator on $SL(2,\mathbb{C})$ starting from a non-Abelian deformation of the natural carrier…

We construct a Lagrangian for general nonlinear electrodynamics that features electric and magnetic potentials on equal footing. In the language of this Lagrangian, discrete and continuous electric-magnetic duality symmetries can be…

We suggest an extension of the Yang-Mills theory which includes non-Abelian tensor gauge fields. The invariant Lagrangian is quadratic in the field strength tensors and describes interaction of charged tensor gauge bosons of arbitrary large…

For any causal nonlinear electrodynamics theory that is "self-dual" (electromagnetic $U(1)$-duality invariant), the Legendre-dual pair of Lagrangian and Hamiltonian densities $\{\mathcal{L},\mathcal{H}\}$ are constructed from functions…

A study of sigma models whose target space is a group G that admits a compatible Poisson structure is presented. The natural action of O(D,D;Z) on the generalised tangent bundle TG+T*G and a generalisation of the Courant bracket that…

We solve the topological Poisson Sigma model for a Poisson-Lie group $G$ and its dual $G^*$. We show that the gauge symmetry for each model is given by its dual group that acts by dressing transformations on the target. The resolution of…

We study a class of duality transformations in generalised Z(2) gauge theories and Ising models on two- and three-dimensional compact lattices. The theories are interpreted algebraically in terms of the structure constants of a…

It it known that to get the usual Hamiltonian formulation of lattice Yang-Mills theory in the temporal gauge $A_{0}=0$ one should place on every link the cotangent bundle of a Lie group. The cotangent bundle may be considered as a limiting…

Employing the gauge-invariant formalism in the two-Higgs-doublet model (THDM) offers profound insights into the model's fundamental structure. A specific set of gauge-invariant bilinear combinations, constructed from the Higgs doublets,…

We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with $1\le p\le D$, which realize an off-shell algebra of bosonic gauge transformations. We show how these tensor hierarchies can be put on-shell…

(0,2) gauged linear sigma models with torsion, corresponding to principal torus bundles over warped CY bases, provide a useful framework for getting exact statements about perturbative dualities in the presence of fluxes. In this context we…

We discuss the problem of the existence of a regular invariant Lagrangian for a given system of invariant second-order differential equations on a Lie group $G$, using approaches based on the Helmholtz conditions. Although we deal with the…

The worldsheet theories that describe Poisson-Lie T-dualisable $\sigma$-models on group manifolds as well as integrable $\eta$, $\lambda$ and $\beta$-deformations provide examples of ${\cal E}$-models. Here we show how such ${\cal…