Non-Abelian Axial-Vector Duality: a Geometric Description

We give a geometric characterization of the quasi axial-vector (Kiritsis-Obers) target space duality in the spirit of the bi-algebra (Klimcik-Severa) approach. We show that the sigma-models constructed by taking quotients have non-abelian chiral currents that obey "non-commutative conservation laws" and provide the criterion for a sigma-model to have a dual using the axial-vector procedure.Comment: 10 pages, plain LaTeX 2e. The paper (and conclusions) is significantly revised due to a misprint in one of the references. If you read the old version, you SHOULD get this on

On Conformal Properties of the Dualized Sigma-Models

We have calculated the first-order beta-functions for a sigma-model ( with dilaton) dualized with respect to an arbitrary Lie group that acts without isotropy. We find that non-abelian duality preserves conformal invariance for semi-simple groups, but in general there is an extra contribution to the beta-function proportional to the trace of the structure constants, which cannot be absorbed into an additional dilaton shift. Two particular examples, a Bianchi V cosmological background and the G \otimes G WZW model, are discussed.Comment: 12 pages, LaTeX 2e with fleqn.sty (removed the Stony Brook emblem which was causing problems

Poisson-Lie T-Duality: the Path-Integral Derivation

We formulate Poisson-Lie T-duality in a path-integral manner that allows us to analyze the quantum corrections. Using the path-integral, we rederive the most general form of a Poisson-Lie dualizeable background and the generalized Buscher transformation rules it has to satisfy.Comment: 16 pages, plain LaTeX 2e, one paragraph added to the conclusions; this is the final version accepted by Physics Letters

Recent developments in non-Abelian T-duality in string theory

We briefly review the essential points of our recent work in non-Abelian T-duality. In particular, we show how non-abelian T-duals can effectively describe infinitely high spin sectors of a parent theory and how to implement the transformation in the presence of non-vanishing Ramond fields in type-II supergravity.Comment: 8 pages, Proceedings contribution to the 10th Hellenic School on Elementary Particle Physics and Gravity, Corfu, Greece, September 201

A New Duality Symmetry in String Theory

We consider the conformal gauging of non-abelian groups. In such cases there are inequivalent ways of gauging (generalizing the axial and vector cases for abelian groups) corresponding to external automorphisms of the group. Different \s-models obtained this way correspond to the same conformal field theory. We use the method of quotients to formulate this equivalence as a new duality symmetry.Comment: LaTeX, 7pp, CERN-TH.7310/94, CPTH-A309.0694 (Some clarifications added

Remarks on Non-Abelian Duality

A class of two-dimensional globally scale-invariant, but not conformally invariant, theories is obtained. These systems are identified in the process of discussing global and local scaling properties of models related by duality transformations, based on non-semisimple isometry groups. The construction of the dual partner of a given model is followed through; non-local as well as local versions of the former are discussed.Comment: 33 pages, CERN-TH.7414/94, RI-9-94, WIS-7-9

Bosonization as Duality

We show that bosonization in two dimensions can be derived as a special case of the duality transformations that have recently been used to good effect in string theory. This allows the construction of the bosonic counterpart of any fermionic theory simply by `following your nose' using the standard duality transformation rules. We work through the bosonization of the Dirac fermion, the massive and massless Thirring models, and a fermion on a cylindrical spacetime as illustrative examples.Comment: plain TeX, 21 page

Perturbative Quantum (In)equivalence of Dual σ\sigma Models in 22 dimensions

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 inequivalent} at two loops to the original ones, (both for the Abelian and the non Abelian duality).Comment: 11 pages, Latex, uses espcrc2.st

Non-Abelian T-duality for open strings

In the first part of the talk we discuss T-duality for a free boson on a world sheet with boundary in a setting suitable for the generalization to non-trivial backgrounds. The gauging method as well as the canonical transformation are considered. In both cases Dirichlet strings as T-duals of Neumann strings arise in a generic way. In the second part the gauging method is employed to construct the T-dual of a model with non-Abelian isometries.Comment: 10 pages, Latex, psfig.sty, one figure; Talk given at the International Symposium on the Theory of Elementary Particles, Buckow 1996, References adde

Poisson-Lie T-duality

A description of dual non-Abelian duality is given, based on the notion of the Drinfeld double. The presentation basically follows the original paper \cite{KS2}, written in collaboration with P. \v Severa, but here the emphasis is put on the algebraic rather than the geometric aspect of the construction and a concrete example of the Borelian double is worked out in detail.Comment: 11 pages, LaTeX, Lecture given at Trieste conference on S-duality and mirror symmetry, June 1995, (signs in Eqs. (10,11) corrected, 1 reference added