Hamilton-Jacobi formulation of holographic entanglement entropy

Jankowski, Jakub

doi:10.1140/epjst/e2020-000042-8

Cited by 4 publications

(2 citation statements)

References 15 publications

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“…In this context, the HJ formulation is very convenient as it gives directly an equation for the on-shell action in terms of boundary data, without having to go through solving the bulk equations of motion. It has been applied extensively to the holographic RG, starting from [23], to Wilson loops [24] and to the entanglement entropy [25,26], among others.…”

Section: Hamilton-jacobi Approachmentioning

confidence: 99%

Holographic entanglement entropy inequalities beyond strong subadditivity

Daguerre

Ginzburg

Torroba

2022

J. High Energ. Phys.

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The vacuum entanglement entropy in quantum field theory provides nonperturbative information about renormalization group flows. Most studies so far have focused on the universal terms, related to the Weyl anomaly in even space-time dimensions, and the sphere free energy F in odd dimensions. In this work we study the entanglement entropy on a sphere of radius R in a large radius limit, for field theories with gravity duals. At large radius the entropy admits a geometric expansion in powers of R; the leading term is the well-known area term, and we also consider the subleading contributions. These terms can be physical, they contain information about the full renormalization group flow, and they reproduce known monotonicity theorems in particular cases. We set up an efficient method for calculating them using the Hamilton-Jacobi equation for the holographic entanglement entropy. We first reproduce the known result for the area term, the coefficient multiplying Rd−2 in the entanglement entropy. We then obtain the holographic result for the Rd−4 term and establish its irreversibility. Finally, we derive the Rd−6 coefficient for holographic theories, and also establish its irreversibility. This result goes beyond what has been proved in quantum field theory based on strong subadditivity, and hints towards new methods for analyzing the monotonicity of the renormalization group in space-time dimensions bigger than four.

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Section: Hamilton-jacobi Approachmentioning

confidence: 99%

Holographic entanglement entropy inequalities beyond strong subadditivity

Daguerre

Ginzburg

Torroba

2022

J. High Energ. Phys.

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“…See also[58] where the author describes the Hamilton-Jacobi formalism for the bulk action dual to the entanglement entropy of a strip in the dual field theory.…”

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confidence: 99%

Inverted c-functions in thermal states

Cartwright

Kaminski

2022

J. High Energ. Phys.

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We first compute the effect of a chiral anomaly, charge, and a magnetic field on the entanglement entropy in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills theory at strong coupling via holography. Depending on the width of the entanglement strip the entanglement entropy probes energy scales from the ultraviolet to the infrared energy regime of this quantum field theory (QFT) prepared in a given state. From the entanglement entropy, we compute holographic c-functions and demonstrate an inverted c-theorem for them. That is, these c-functions in generic thermal states monotonically increase towards the infrared (IR) energy regime. This is in contrast to the c-functions in vacuum states which decrease along the renormalization group flow towards the IR regime of a renormalizable QFT. Furthermore, in thermal states and in the IR limit, the c-functions behave thermally, growing proportionally to the value of the thermal entropy. The chiral anomaly affects the c-functions more in the IR regime, and its effect is peaked at an intermediate value of the magnetic field at a fixed chemical potential and temperature.

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