Perturbative Instabilities on the Non-Commutative Torus, Morita Duality and Twisted Boundary Conditions

TL;DR

This paper investigates one-loop quantum corrections in scalar and gauge theories on the non-commutative torus, revealing stability properties, instabilities, and their implications for symmetry breaking through Morita duality and twisted boundary conditions.

Contribution

It demonstrates how Morita equivalence relates non-commutative theories to commutative ones with twisted boundary conditions, analyzing quantum corrections and instabilities.

Findings

UV/IR mixing does not cause singularities.

Gauge theories exhibit tachyonic instabilities.

Instabilities relate to symmetry breaking via electric flux condensation.

Abstract

We study one-loop corrections in scalar and gauge field theories on the non-commutative torus. For rational theta, Morita equivalence allows these theories to be reformulated in terms of ordinary theories on a commutative torus with twisted boundary conditions. UV/IR mixing does not lead to singularities, however there can be large corrections. In particular, gauge theories show tachyonic instabilities for some of the modes. We discuss their relevance to spontaneous Z_N x Z_N symmetry breaking in the Morita dual SU(N) theory due to electric flux condensation.