Lattice gluodynamics at negative g^2

TL;DR

This paper explores SU(N) lattice gauge theory at negative coupling values, revealing phase transitions, dominant configurations, and relations between observables at positive and negative couplings, with implications for understanding non-perturbative phenomena.

Contribution

It introduces a detailed analysis of lattice gauge theory at negative g^2, identifying dominant configurations and phase transitions, and establishes relations between observables across different coupling regimes.

Findings

Dominant configurations at negative g^2 involve center elements on non-intersecting lines.

Discontinuity in the average plaquette prevents a convergent series in g^2.

Evidence of an Ising-like first order phase transition near beta=-22.

Abstract

We consider Wilson's SU(N) lattice gauge theory (without fermions) at negative values of beta= 2N/g^2 and for N=2 or 3. We show that in the limit beta -> -infinity, the path integral is dominated by configurations where links variables are set to a nontrivial element of the center on selected non intersecting lines. For N=2, these configurations can be characterized by a unique gauge invariant set of variables, while for N=3 a multiplicity growing with the volume as the number of configurations of an Ising model is observed. In general, there is a discontinuity in the average plaquette when g^2 changes its sign which prevents us from having a convergent series in g^2 for this quantity. For N=2, a change of variables relates the gauge invariant observables at positive and negative values of beta. For N=3, we derive an identity relating the observables at beta with those at beta rotated by +- 2pi/3 in the complex plane and show numerical evidence for a Ising like first order phase transition near beta=-22. We discuss the possibility of having lines of first order phase transitions ending at a second order phase transition in an extended bare parameter space.