Entanglement entropy and Page curve from the ${\cal M}$-theory dual of thermal QCD above $T_c$ at intermediate coupling

Gopal Yadav; Aalok Misra

doi:10.1103/PhysRevD.107.106015

paper

Entanglement entropy and Page curve from the $M$ -theory dual of thermal QCD above $T_{c}$ at intermediate coupling

arXiv:2207.04048 · doi:10.1103/PhysRevD.107.106015

Abstract

Obtaining the Page curve in the context of eternal black holes associated with top-down non-conformal holographic thermal duals at intermediate coupling, has been entirely unexplored in the literature. We fill this gap in the context of a doubly holographic setup relevant to the M-theory dual of thermal QCD-like theories at $T > T_{c}$ at intermediate coupling. Remarkably, excluding the higher derivative terms, the entanglement entropy(EE) of the Hawking radiation from the on-shell Wald EE (for appropriate choices of constants of integration appearing in the embeddings) increases almost linearly with the boundary time due to dominance of EE contribution from the Hartman-Maldacena(HM)-like surface $S_{E E}^{H M, β^{0}}, β \sim l_{p}^{6}$ . Curiously, this imparts a "Swiss-Cheese" structure to the surface $S_{E E}^{H M, β^{0}}$ at a given time (less than the Page time $t_{P}$ ), in $R_{\geq 0} \times C$ effecting what could be dubbed as a "Large N Scenario" (LNS). Then, after $t_{P}$ , the EE contribution from the Island Surface (IS) $S_{E E}^{I S, β^{0}}$ dominates and saturates the linear time growth of the EE of Hawking radiation and leads to the Page curve. Requiring $S_{E E}^{I S, β^{0}} / S_{B H} \sim 2$ up to LO in the non-conformal analog of " $c G_{N}^{(11)} / r_{h}^{9}$ ", and positivity of $t_{P}$ , set respectively a lower and upper bound on the horizon radius $r_{h}$ (the non-extremality parameter). With the inclusion of the $O (R^{4})$ terms in M theory, the turning point associated with the HM-like surface/IS being in the deep IR, results in a relationship between $l_{p}$ and $r_{h}$ along with a conjectural $e^{- O (1) N^{1/3}}$ -suppression (motivated by $S_{E E}^{I S, β^{0}} / S_{B H} \sim 2$ ). We obtain a hierarchy with respect to this N-dependent exponential in $S_{E E}^{H M, β^{0}}, S_{E E}^{I S, β^{0}} (O (β^{0}))$ and $S_{E E}^{H M, β}, S_{E E}^{H M, β} (O (β))$ .

arXiv commentv4:1+77 Pages, LaTeX, 11 figures; title changed; Explanatory text added; to appear in PRD

Entanglement entropy and Page curve from the $M$ -theory dual of thermal QCD above $T_{c}$ at intermediate coupling

Abstract

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Entanglement entropy and Page curve from the M-theory dual of thermal QCD above Tc​ at intermediate coupling

Abstract

References in corpus (60)

Cited by in corpus (6)

Entanglement entropy and Page curve from the $M$ -theory dual of thermal QCD above $T_{c}$ at intermediate coupling