D-dependence of gap between critical temperatures in one-dimensional gauge theories

TL;DR

This paper studies how the temperature gap between phase transitions in large-N bosonic gauge theories varies with the number of dimensions, revealing an opposite trend to gravity and fluid analogies, challenging existing correspondences.

Contribution

It provides a detailed analysis of the D-dependence of critical temperature gaps in gauge theories, offering a counterexample to gauge/gravity and gauge/fluid dualities.

Findings

The D-dependence of the temperature gap is opposite to that in gravity and fluid systems.

The results challenge the expected universality of gauge/gravity and gauge/fluid correspondences.

The study uses the 1/D expansion equations for critical temperatures in large-N gauge theories.

Abstract

We investigate the dimensional dependence (D-dependence) of the difference (gap) between the critical temperatures associated with the uniform/non-uniform and non-uniform/gapped transitions in the large-N bosonic gauge theories with D matrix scalar fields on a circled space. We use the equations describing these critical temperatures given in the 1/D expansion arXiv:0910.4526. These transitions are related with Gregory-Laflamme instabilities in the gravities and Rayleigh-Plateau instabilities in the fluid dynamics, and qualitative similarities between these are expected. We find that the tendency in the D-dependence of the gap is opposite from those in the gravity and fluid side. This is interesting as a counterexample to the gauge/gravity and gauge/fluid correspondences.