Compact lattice U(1) and Seiberg-Witten duality

TL;DR

This paper reconciles numerical and analytical perspectives on the phase transition in compact U(1) lattice gauge theory, showing that quantum corrections turn an expected second order transition into a weakly first order one.

Contribution

It demonstrates that incorporating radiative corrections via the Coleman-Weinberg mechanism explains the first order transition observed numerically, aligning theory with simulation results.

Findings

Numerical simulations confirm a weakly first order phase transition.

Analytical analysis shows radiative corrections induce a first order transition.

The Coleman-Weinberg mechanism explains the transition's nature.

Abstract

Simulations in compact U(1) lattice gauge theory in 4D show now beyond any reasonable doubts that the phase transition separating the Coulomb from the confined phase is of first order, albeit a very weak one. This settles the issue from the numerical side. On the analytical side, it was suggested some time ago, based on the qualitative analogy between the phase diagram of such a model and the one of scalar QED obtained by soft breaking the N=2 Seiberg-Witten model down to N=0, that the phase transition should be of second order. In this work we take a fresh look at this issue and show that a proper implementation of the Seiberg-Witten model below the supersymmetry breaking scale requires considering some new radiative corrections. Through the Coleman-Weinberg mechanism this turns the second order transition into a weakly first order one, in agreement with the numerical results. We comment on several other aspects of this continuum model.