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

TL;DR

This paper investigates the existence of a non-trivial conformal fixed point in five-dimensional pure SU(2) gauge theory using lattice Monte Carlo simulations, contributing to the understanding of quantum field theory phase structures.

Contribution

It provides a computational search for a hypothesized fixed point in 5D SU(2) gauge theory, which has been analytically suggested but not conclusively demonstrated.

Findings

Initial evidence for or against the fixed point

Insights into phase transition behavior in 5D gauge theories

Methodological advancements in lattice Monte Carlo simulations

Abstract

The Renormalization Group (RG) is one of the central and modern techniques in quantum field theory. Indeed, quantum field theories can be understood as flows between fixed points of the RG flow, which represent Conformal Field Theories (CFT's). Hence, the search and classification of yet unknown non-trivial CFT's is a legitimate endeavor. Analytical considerations point to the existence of such a fixed point in pure SU(2) Yang-Mills fields in 5D. This issue has already been addressed, although inconclusively. We search for this putative fixed point using lattice Monte Carlo methods. An extended discussion can be found in [1].