2d affine XY-spin model/ 4d gauge theory duality and deconfinement

TL;DR

This paper establishes a duality between 2D XY-spin models with symmetry-breaking perturbations and 4D SU(2) gauge theories on a small circle, enabling the study of deconfinement transitions using spin system techniques.

Contribution

It introduces a novel duality linking 2D XY-spin models to 4D gauge theories, facilitating analysis of deconfinement and chiral transitions.

Findings

Duality maps topological defects to gauge theory particles.

Spin vortices correspond to W-bosons in gauge theories.

The approach applies to theories with adjoint Weyl fermions.

Abstract

We introduce a duality between two-dimensional XY-spin models with symmetry-breaking perturbations and certain four-dimensional SU(2)and SU(2)/Z_2 gauge theories, compactified on a small spatial circle R^(1,2) x S^1, and considered at temperatures near the deconfinement transition. In a Euclidean set up, the theory is defined on R^2 x T^2. Similarly, thermal gauge theories of higher rank are dual to new families of "affine" XY-spin models with perturbations. For rank two, these are related to models used to describe the melting of a 2d crystal with a triangular lattice. The connection is made through a multi-component electric-magnetic Coulomb gas representation for both systems. Perturbations in the spin system map to topological defects in the gauge theory, such as monopole-instantons or magnetic bions, and the vortices in the spin system map to the electrically charged W-bosons in field theory (or vice versa, depending on the duality frame). The duality permits one to use the two-dimensional technology of spin systems to study the thermal deconfinement and discrete chiral transitions in four-dimensional SU(N) gauge theories with n_f >=1 adjoint Weyl fermions.