Entanglement entropy, dualities, and deconfinement in gauge theories

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 S 1 L evades these difficulties. In particular, we study Yang-Mills theory on R 3 × S 1 L 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 Z p 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.

Study of center and chiral symmetry realization in thermal N=1 super Yang-Mills theory using the gradient flow

“…The same constraint was also found from anomaly matching for SU(N c ) with adjoint and fundamental matter in [42]. Our results indicate that this inequality is saturated, as predicted remarkably for adjoint QCD and SYM on R 3 × S 1 in [43,44,45,46]. An interesting final quantity determined by our study is the deconfinement temperature in the chiral/supersymmetric limit.…”

Interplay between the holographic QCD phase diagram and entanglement entropy

“…In particular, a phase transition between connected and disconnected entangling surfaces as a function of size of the entangling surface, at which the order of the entanglement entropy changes, was suggested as a signature of (de)confinement. This idea was then generalized to a variety of confining systems [55][56][57][58][59][60][61], and has moreover received numerical confirmation from the aforementioned lattice papers [52][53][54], see also [62]. In [63], we performed a similar analysis including a background magnetic field and showed for the first time an anisotropic footprint of confinement/deconfinement transition in the entanglement entropy.…”

Lattice study of Rényi entanglement entropy in SU(Nc) lattice Yang-Mills theory with NRabenstein1, Bodendorfer2, Schäfer3 et al. 2019Phys. Rev. D271100View full textAdd to dashboardCite

“…of states [11]. In the vicinity of a second-order thermal phase transition in SU (2) gauge theory one can expect an enhancement of entanglement entropy and its fluctuations due to the divergence of correlation length [38], which is absent for first-order finite-temperature transitions in SU (N c > 2) gauge theories.…”