Compact lattice U(1) and Seiberg-Witten duality: a quantitative comparison

TL;DR

This paper quantitatively compares the effective scalar QED description of the Coulomb-confinement transition in compact U(1) lattice gauge theory with numerical results, supporting the Seiberg-Witten duality conjecture.

Contribution

It provides a detailed analysis and quantitative validation of the conjecture linking the Coulomb-confinement transition to scalar QED derived from Seiberg-Witten theory.

Findings

Quantitative agreement with monopole and dual photon mass measurements near phase transition

Supports the Seiberg-Witten duality conjecture in lattice gauge theory

Provides detailed analysis of the effective description in strong coupling regime

Abstract

It was conjectured some time ago that an effective description of the Coulomb-confinement transition in compact U(1) lattice gauge field theory could be described by scalar QED obtained by soft breaking of the N=2 Seiberg-Witten model down to N=0 in the strong coupling region where monopoles are light. In two previous works this idea was presented at a qualitative level. In this work we analyze in detail the conjecture and obtain encouraging quantitative agreement with the numerical determination of the monopole mass and the dual photon mass in the vicinity of the Coulomb to confining phase transition.