Dominance of a single topological sector in gauge theory on non-commutative geometry

TL;DR

This paper shows that in 2D non-commutative U(1) gauge theory, a single topological sector dominates in the continuum limit, unlike in commutative space-time, with implications for string theory and field theory.

Contribution

It introduces a new finite-matrix formulation for studying topological properties of NC gauge theory and reveals the dominance of one topological sector in the continuum limit.

Findings

Single topological sector dominates in NC gauge theory

Contrast with commutative space-time where all sectors appear

Implications for string theory compactifications

Abstract

We demonstrate a striking effect of non-commutative (NC) geometry on topological properties of gauge theory by Monte Carlo simulations. We study 2d U(1) NC gauge theory for various boundary conditions using a new finite-matrix formulation proposed recently. We find that a single topological sector dictated by the boundary condition dominates in the continuum limit. This is in sharp contrast to the results in commutative space-time based on lattice gauge theory, where all topological sectors appear with certain weights in the continuum limit. We discuss possible implications of this effect in the context of string theory compactifications and in field theory contexts.