SU(2) lattice gauge theory in 2+1 dimensions: critical couplings from twisted boundary conditions and universality

TL;DR

This paper precisely determines the critical coupling for the deconfinement transition in 2+1D SU(2) gauge theory using universality and boundary conditions, linking lattice results with the 2D Ising model.

Contribution

It introduces a method to accurately find the critical coupling by intersecting vortex free energy with known Ising model values, enhancing understanding of phase transitions in gauge theories.

Findings

Critical coupling beta_c determined with high precision.

Demonstrates universality between SU(2) gauge theory and 2D Ising model.

Provides data on how beta varies with temperature for different lattice sizes.

Abstract

We present a precision determination of the critical coupling beta_c for the deconfinement transition in pure SU(2) gauge theory in 2+1 dimensions. This is possible from universality, by intersecting the center vortex free energy as a function of the lattice coupling beta with the exactly known value of the interface free energy in the 2D Ising model at criticality. Results for lattices with different numbers of sites N_t along the Euclidean time direction are used to determine how beta varies with temperature for a given N_t around the deconfinement transition.