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 ${\mathbb{S}}_L^1$ S L 1 evades these difficulties. In particular, we study Yang-Mills theory on ${\mathrm{\mathbb{R}}}^3\times {\mathbb{S}}_L^1$ ℝ 3 × 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 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.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 $$ {\mathbb{S}}_L^1 $$ S L 1 evades these difficulties. In particular, we study Yang-Mills theory on $$ {\mathrm{\mathbb{R}}}^3\times {\mathbb{S}}_L^1 $$ ℝ 3 × 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 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.

arXiv:1804.01956Journal of High Energy PhysicsAug 1, 201812 citations

Hidden Fermi surfaces in compressible states of gauge-gravity duality

Liza Huijse, Subir Sachdev A, Brian G. Swingle

General scaling arguments, and the behavior of the thermal entropy density, are shown to lead to an infrared metric holographically representing a compressible state with hidden Fermi surfaces. This metric is characterized by a general dynamic critical exponent, $z$ , and a specific hyperscaling violation exponent, $\ensuremath{\theta}$. The same metric exhibits a logarithmic violation of the area law of entanglement entropy, as shown recently by Ogawa et al. [e-print arXiv:1111.1023 (unpublished)]. We study the dependence of the entanglement entropy on the shape of the entangling region(s), on the total charge density, on temperature, and on the presence of additional visible Fermi surfaces of gauge-neutral fermions; for the latter computations, we realize the needed metric in an Einstein-Maxwell-dilaton theory. All our results support the proposal that the holographic theory describes a metallic state with hidden Fermi surfaces of fermions carrying gauge charges of deconfined gauge fields.General scaling arguments, and the behavior of the thermal entropy density, are shown to lead to an infrared metric holographically representing a compressible state with hidden Fermi surfaces. This metric is characterized by a general dynamic critical exponent, $z$, and a specific hyperscaling violation exponent, $\ensuremath{\theta}$. The same metric exhibits a logarithmic violation of the area law of entanglement entropy, as shown recently by Ogawa et al. [e-print arXiv:1111.1023 (unpublished)]. We study the dependence of the entanglement entropy on the shape of the entangling region(s), on the total charge density, on temperature, and on the presence of additional visible Fermi surfaces of gauge-neutral fermions; for the latter computations, we realize the needed metric in an Einstein-Maxwell-dilaton theory. All our results support the proposal that the holographic theory describes a metallic state with hidden Fermi surfaces of fermions carrying gauge charges of deconfined gauge fields.

arXiv:1112.0573Physical Review BJan 25, 2012399 citations

Entanglement entropy in gauge theories and the holographic principle for electric strings

P. V. Buividovich, M. I. Polikarpov

arXiv:0806.3376Physics Letters BOct 29, 2008215 citations

Entanglement and thermal entropy of gauge fields

Christopher Eling, Yaron Oz, Stefan Theisen

arXiv:1308.4964Journal of High Energy PhysicsNov 1, 201327 citations

Emergent Bulk Gauge Field in Random Tensor Networks

Xiao-Liang Qi

Random tensor network states are toy models for holographic duality, which have entanglement properties determined by graph geometry. In this paper, we propose a generalization of the random tensor network states which describe an ensemble of states preserving a given global symmetry. We show that Renyi entropy for this family of states can be described by a quantum extremal surface formula, with corrections to the area law term determined by a bulk gauge theory wavefunction. This provides a toy model of the correspondence between boundary global symmetry and bulk gauge symmetry in holographic duality. We discuss the boundary physical consequences of the bulk deconfined and confined phases.Random tensor network states are toy models for holographic duality, which have entanglement properties determined by graph geometry. In this paper, we propose a generalization of the random tensor network states which describe an ensemble of states preserving a given global symmetry. We show that Renyi entropy for this family of states can be described by a quantum extremal surface formula, with corrections to the area law term determined by a bulk gauge theory wavefunction. This provides a toy model of the correspondence between boundary global symmetry and bulk gauge symmetry in holographic duality. We discuss the boundary physical consequences of the bulk deconfined and confined phases.

arXiv:2209.02940WORLD SCIENTIFIC eBooksSep 7, 20223 citations

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

S L 1 evades these difficulties. In particular, we study Yang-Mills theory on

{\mathrm{\mathbb{R}}}^3\times {\mathbb{S}}_L^1

ℝ 3 × 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 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.

z

, and a specific hyperscaling violation exponent, $\ensuremath{\theta}$. The same metric exhibits a logarithmic violation of the area law of entanglement entropy, as shown recently by Ogawa et al. [e-print arXiv:1111.1023 (unpublished)]. We study the dependence of the entanglement entropy on the shape of the entangling region(s), on the total charge density, on temperature, and on the presence of additional visible Fermi surfaces of gauge-neutral fermions; for the latter computations, we realize the needed metric in an Einstein-Maxwell-dilaton theory. All our results support the proposal that the holographic theory describes a metallic state with hidden Fermi surfaces of fermions carrying gauge charges of deconfined gauge fields.