Remarks on effective action and entanglement entropy of Maxwell field in generic gauge

We review the results of refs. [1,2], in which the entanglement entropy in spaces with horizons, such as Rindler or de Sitter space, is computed using holography. This is achieved through an appropriate slicing of anti-de Sitter space and the implementation of a UV cutoff. When the entangling surface coincides with the horizon of the boundary metric, the entanglement entropy can be identified with the standard gravitational entropy of the space. For this to hold, the effective Newton's constant must be defined appropriately by absorbing the UV cutoff. Conversely, the UV cutoff can be expressed in terms of the effective Planck mass and the number of degrees of freedom of the dual theory. For de Sitter space, the entropy is equal to the Wald entropy for an effective action that includes the higher-curvature terms associated with the conformal anomaly. The entanglement entropy takes the expected form of the de Sitter entropy, including logarithmic corrections.

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Wilsonian Effective Action and Entanglement Entropy

Symmetry ◽

10.3390/sym13071221 ◽

2021 ◽

Vol 13 (7) ◽

pp. 1221

Author(s):

Satoshi Iso ◽

Takato Mori ◽

Katsuta Sakai

Keyword(s):

Renormalization Group ◽

Gauge Theory ◽

Effective Action ◽

Correlation Functions ◽

Entanglement Entropy ◽

Feynman Diagrams ◽

Field Theories ◽

Quantum Field Theories ◽

Quantum Field ◽

Non Gaussian

This is a continuation of our previous works on entanglement entropy (EE) in interacting field theories. In previous papers, we have proposed the notion of ZM gauge theory on Feynman diagrams to calculate EE in quantum field theories and shown that EE consists of two particular contributions from propagators and vertices. We have also shown that the purely non-Gaussian contributions from interaction vertices can be interpreted as renormalized correlation functions of composite operators. In this paper, we will first provide a unified matrix form of EE containing both contributions from propagators and (classical) vertices, and then extract further non-Gaussian contributions based on the framework of the Wilsonian renormalization group. It is conjectured that the EE in the infrared is given by a sum of all the vertex contributions in the Wilsonian effective action.

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Renormalization of entanglement entropy and the gravitational effective action

Journal of High Energy Physics ◽

10.1007/jhep12(2014)045 ◽

2014 ◽

Vol 2014 (12) ◽

Cited By ~ 20

Author(s):

Joshua H. Cooperman ◽

Markus A. Luty

Keyword(s):

Effective Action ◽

Entanglement Entropy

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Entanglement entropy for a Maxwell field: Numerical calculation on a two-dimensional lattice

Physical Review D ◽

10.1103/physrevd.90.105013 ◽

2014 ◽

Vol 90 (10) ◽

Cited By ~ 14

Author(s):

Horacio Casini ◽

Marina Huerta

Keyword(s):

Numerical Calculation ◽

Entanglement Entropy ◽

Maxwell Field ◽

Two Dimensional ◽

Dimensional Lattice

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Enhanced corrections near holographic entanglement transitions: a chaotic case study

Journal of High Energy Physics ◽

10.1007/jhep11(2020)007 ◽

2020 ◽

Vol 2020 (11) ◽

Cited By ~ 1

Author(s):

Xi Dong ◽

Huajia Wang

Keyword(s):

Phase Transition ◽

Effective Action ◽

Rotational Symmetry ◽

Entanglement Entropy ◽

Saddle Points ◽

System Size ◽

Entire System ◽

Replica Symmetry ◽

Fixed Area

Abstract Recent work found an enhanced correction to the entanglement entropy of a subsystem in a chaotic energy eigenstate. The enhanced correction appears near a phase transition in the entanglement entropy that happens when the subsystem size is half of the entire system size. Here we study the appearance of such enhanced corrections holo-graphically. We show explicitly how to find these corrections in the example of chaotic eigenstates by summing over contributions of all bulk saddle point solutions, including those that break the replica symmetry. With the help of an emergent rotational symmetry, the sum over all saddle points is written in terms of an effective action for cosmic branes. The resulting Renyi and entanglement entropies are then naturally organized in a basis of fixed-area states and can be evaluated directly, showing an enhanced correction near holographic entanglement transitions. We comment on several intriguing features of our tractable example and discuss the implications for finding a convincing derivation of the enhanced corrections in other, more general holographic examples.

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