Gauge Spinors and String Duality

TL;DR

This paper explores the global formulation of T-duality in heterotic string theories with broken gauge groups, focusing on the role of spinor representations and potential obstructions to duality on complex manifolds.

Contribution

It introduces a global framework for T-duality considering non-existence of generalized spin structures in heterotic string theories with broken gauge groups.

Findings

Global formulation of T-duality for broken gauge groups

Identification of obstructions to duality on complex manifolds

Analysis of spinor representations in string dualities

Abstract

When the gauge groups of the two heterotic string theories are broken, over tori, to their "SO(16)x SO(16)" subgroups, the winding modes correspond to representations which are spinorial with respect to those subgroups. Globally, the two subgroups are isomorphic neither to SO(16)x SO(16) nor to each other. Any attempt to formulate the T-duality of the two theories on any manifold more complicated than the product of a circle with a Euclidean space must therefore take into account the possible non-existence of the relevant "generalised spin structure". We give here a global formulation of T-duality in this case, and discuss examples where the duality seems to be obstructed.