Abstract
Computing the entanglement entropy in confining gauge theories is often accompanied by puzzles and ambiguities. In this work we show that compactifying the theory on a small circle {mathbb{S}}_L^1 evades these difficulties. In particular, we study Yang-Mills theory on {mathrm{mathbb{R}}}^3times {mathbb{S}}_L^1 with double-trace deformations or adjoint fermions and hold it at temperatures near the deconfinement transition. This theory is dual to a multi-component (electric-magnetic) Coulomb gas that can be mapped either to an XY-spin model with ℤp symmetry-preserving perturbations or dual Sine-Gordon model. The entanglement entropy of the dual Sine-Gordon model exhibits an extremum at the critical temperature/crossover. We also compute Rényi mutual information (RMI) of the XY-spin model by means of the replica trick and Monte Carlo simulations. These are expensive calculations, since one in general needs to suppress lower winding vortices that do not correspond to physical excitations of the system. We use a T-duality that maps the original XY model to its mirror image, making the extraction of RMI a much efficient process. Our simulations indicate that RMI follows the area law scaling, with subleading corrections, and this quantity can be used as a genuine probe to detect deconfinement transitions. We also discuss the effect of fundamental matter on RMI and the implications of our findings in gauge theories and beyond.
Highlights
These cases quantities like entanglement entropy and mutual information are indispensable for studying various quantum and classical phase transitions
Unlike the Svetitsky and Yaffe classification of the deconfinement transition [32], which is based on modeling the center symmetry of the gauge group using a scalar field theory, the gauge theory/XY-spin model duality is an exact mapping between both sides of the duality, at least within the validity of the Coulomb gas as an effective field description of gauge theory
In this paper we studied the deconfinement transition in Yang-Mills theory on R2 × T2 by means of information-theoretic techniques in the continuum and on the lattice
Summary
We consider SU(2) Yang-Mills theory compactified over a circle S1L with circumference L, which is taken to be much smaller than the strong coupling scale, i.e., LΛQCD 1:. TrF eiLA33τ3 is the fundamental Polyakov loop wrapping around the circle, and we have chosen the gauge field A3 to lie along the third direction in the color space.. TrF eiLA33τ3 is the fundamental Polyakov loop wrapping around the circle, and we have chosen the gauge field A3 to lie along the third direction in the color space.2 This theory is known as deformed Yang-Mills, or dYM for short. The other method we can use in order to preserve the center symmetry is to add fermions in the adjoint representation of the gauge group and give them periodic boundary conditions along S1L. We can always counter act this effect by taking the coefficient a in (2.2) to be large enough We call this theory deformed Yang-Mills with fundamentals, or dYM(F) for short
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