2d Affine XY-Spin Model/4d Gauge Theory Duality and Deconfinement

We introduce a duality between two-dimensional XY-spin models with symmetry-breaking perturbations and certain four-dimensional SU(2) and SU(2) = Z2 gauge theories, compactified on a small spatial circle R1,2 x S1, and considered at temperatures near the deconfinement transition. In a Euclidean set up, the theory is defined on R2 x T2. 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(Nc) gauge theories with nf (ge) 1 adjoint Weyl fermions.