Symmetry Breaking In Twisted Eguchi-Kawai Models

TL;DR

This paper provides numerical evidence that the centre symmetry in four-dimensional twisted Eguchi-Kawai models with SU(N) gauge groups spontaneously breaks at large N, impacting the models' validity for large N.

Contribution

It demonstrates the spontaneous breaking of centre symmetry in twisted Eguchi-Kawai models at large N and discusses implications for space-time reduction techniques.

Findings

Centre symmetry breaks spontaneously for N ≥ 100.

No confined or deconfined phases observed for N ≤ 144.

Possible interpretation involves 'fluxon' configurations.

Abstract

We present numerical evidence for the spontaneous breaking of the centre symmetry of four-dimensional twisted Eguchi-Kawai models with SU(N) gauge group and symmetric twist, for sufficiently large N. We find that for N greater or equal than 100 this occurs for a wide range of bare couplings. Moreover for N less or equal than 144, where we have been able to perform detailed calculations, there is no window of couplings where the physically interesting confined and deconfined phases appear in the reduced model. We provide a possible interpretation for this in terms of generalised 'fluxon' configurations. We discuss the implications of our findings for the validity and utility of space-time reduced models as N goes to infinity.