Searching for continuous phase transitions in 5D SU(2) lattice gauge theory

TL;DR

This study investigates the phase diagram of 5D SU(2) lattice gauge theory with extended actions to identify potential continuous phase transitions, using Monte Carlo simulations to analyze entropy derivatives near the confinement transition.

Contribution

It explores two extended lattice actions in 5D SU(2) gauge theory to search for continuous phase transitions, providing new insights into the phase structure.

Findings

Excluded second order transition in model i)

Inconclusive results for some regions of model ii)

Used Monte Carlo sampling on lattices up to 12^5

Abstract

We study the phase diagram of 5-dimensional $SU(2)$ Yang-Mills theory on the lattice. We consider two extensions of the fundamental plaquette Wilson action in the search for the continuous phase transition suggested by the $4+\epsilon$ expansion. The extensions correspond to new terms in the action: i) a unit size plaquette in the adjoint representation or ii) a two-unit sided square plaquette in the fundamental representation. We use Monte Carlo to sample the first and second derivative of the entropy near the confinement phase transition, with lattices up to $12^{5}$. While we exclude the presence of a second order phase transition in the parameter space we sampled for model i), our data is not conclusive in some regions of the parameter space of model ii).