Topological Aspects of an Antisymmetric Background Field on Orbifolds

TL;DR

This paper explores how antisymmetric background fields in string theory on orbifolds act as topological terms, revealing new quantum behaviors and anomalies in the models.

Contribution

It provides a detailed analysis of topological effects of antisymmetric background fields on orbifold string theories, highlighting novel quantum anomalies and modifications.

Findings

Zero mode variables obey nontrivial quantization conditions

Coordinate transformations are modified at quantum level

Wave functions acquire nontrivial phases around non-contractible loops

Abstract

We study string theory on orbifolds in the presence of an antisymmetric constant background field in detail and discuss some of new aspects of the theory. It is pointed out that the term with the antisymmetric background field can be regarded as a topological term like a Chern-Simons term or a Wess-Zumino term. Detailed analysis in the operator formalism shows that orbifold models with topologically nontrivial twists exhibit various anomalous behavior: Zero mode variables obey nontrivial quantization conditions. Coordinate transformations which define orbifolds are modified at quantum level. Wave functions of twisted strings in general acquire nontrivial phases when they move around non-contractible loops on orbifolds. Zero mode eigenvalues are shifted from naively expected values, in favor of modular invariance.