Vector Induced Lattice Gauge Theories

TL;DR

This paper explores vector induced lattice gauge theories, revealing their phase behavior at different temperatures and their critical dimensions, with implications for understanding gauge theories and related models.

Contribution

It introduces the analysis of vector induced lattice gauge theories, especially QED induced models, and identifies their critical behavior at specific dimensions and temperature regimes.

Findings

At negative temperature, models correspond to the dimer problem.

At positive temperature, models describe a gas of branched polymers with loops.

Models are critical at dimension six for finite N, but not for infinite N.

Abstract

We consider vector induced lattice gauge theories, in particular we consider the QED induced and we show that at negative temperature corresponds to the dimer problem while at positive temperature it describes a gas of branched polymers with loops. We argue that these models are critical at $D_{cr}=6$ for $N\ne\infty$ and they are {\sl not} critical for $N=\infty$.