T-Duality in Lattice Regularized Sigma Models

TL;DR

This paper demonstrates that Abelian T-duality persists in lattice regularized bosonic string models when formulated with single-valued fields, and explores generalized T-duality involving topological sectors and higher-dimensional models.

Contribution

It shows the survival of T-duality in lattice models with a new projection method and introduces generalized dualities involving topological and higher-dimensional gauge theories.

Findings

T-duality is preserved in lattice regularized models for strings on a circle.

A generalized T-duality exchanges target space and cohomology groups.

Models with higher-dimensional variables exhibit T-duality with topological sector summations.

Abstract

It is shown that when the underlying sigma model of bosonic string theory is written in terms of single-valued fields, which live in the covering space of the target space, Abelian T-duality survives lattice regularization of the world-sheet. The projection onto the target-space is implemented through a sum over cohomology, which bears resemblance to summing over topological sectors in Yang-Mills theories. In particular, the case of string theory on a circle is shown to be explicitly self-dual in the lattice regulated model and automatically forbids vortex excitations which would otherwise destroy the duality. For other target spaces a generalized notion of T-duality is observed in which the target space and the cohomology coefficient group are interchanged under duality. Specific examples show that the fundamental group of the target space may not be preserved in the T-dual theory. Generalized models which exhibit T-duality behaviour, with dynamical variables that live on the k-dimensional cells of (p+1)-dimensional world-volumes, are also constructed. These models correspond to gauge theories, and higher-dimensional analogues, in which one sums over various topological sectors of the theory.