Holographic renormalization group flows and boundary conformal field theories

135

245

In this note, we explore the possibility that certain high-energy holographic CFT states correspond to black hole microstates with a geometrical behind-the-horizon region, modelled by a portion of a second asymptotic region terminating at an end-of-theworld (ETW) brane. We study the time-dependent physics of this behind-the-horizon region, whose ETW boundary geometry takes the form of a closed FRW spacetime. We show that in many cases, this behind-the-horizon physics can be probed directly by looking at the time dependence of entanglement entropy for sufficiently large spatial CFT subsystems. We study in particular states defined via Euclidean evolution from conformal boundary states and give specific predictions for the behavior of the entanglement entropy in this case. We perform analogous calculations for the SYK model and find qualitative agreement with our expectations.A fascinating possibility is that for certain states, we might have gravity localized to the ETW brane as in the Randall-Sundrum II scenario for cosmology. In this case, the effective description of physics beyond the horizon could be a big bang/big crunch cosmology of the same dimensionality as the CFT. In this case, the d-dimensional CFT describing the black hole microstate would give a precise, microscopic description of the d-dimensional cosmological physics. seancooper@phas.ubc.ca, rozali@phas.ubc.ca, bswingle@umd.edu, mav@phas.ubc.ca, cwaddell@phas.ubc.ca, daw@phas.ubc.ca 2 Some authors have argued that quantum effects should modify these expectations: the "fuzzball" proposal [1,2,3,4] suggests that microstate geometries are actually horizonless, while proponents of the "firewall" scenario [5,6] argued that consistency with unitarity and the equivalence principle imply that the geometry must end in some type of singularity at or just beyond the horizon. But many authors have given counter-arguments suggesting a more conventional picture.

Section: Discussionmentioning

confidence: 99%

Black hole microstate cosmology

Cooper

Rozali

Swingle

et al. 2019

135

245

“…Many gravity solutions exist that describe RG flows between DCFTs, usually involving "probe" defects, meaning the defect's contributions to observables (including EE) are suppressed by factors of N relative to the ambient CFT [24]. Few solutions exist describing conformal defects outside of the probe limit [25][26][27]. Some ad hoc solutions for the holographic duals of BCFTs, and RG flows between BCFTs, appear in refs.…”

Section: Jhep05(2014)084mentioning

confidence: 99%

“…Some ad hoc solutions for the holographic duals of BCFTs, and RG flows between BCFTs, appear in refs. [25,[28][29][30]. 2 In some cases these are genuine solutions of SUGRA theories [29], and hence we have good reason to believe a pathology-free dual BCFT actually exists.…”

Section: Jhep05(2014)084mentioning

confidence: 99%

On holographic defect entropy

Estes

Jensen

O’Bannon

et al. 2014

121

Abstract:We study a number of (3+1)-and (2+1)-dimensional defect and boundary conformal field theories holographically dual to supergravity theories. In all cases the defects or boundaries are planar, and the defects are codimension-one. Using holography, we compute the entanglement entropy of a (hemi-)spherical region centered on the defect (boundary). We define defect and boundary entropies from the entanglement entropy by an appropriate background subtraction. For some (3 + 1)-dimensional theories we find evidence that the defect/boundary entropy changes monotonically under certain renormalization group flows triggered by operators localized at the defect or boundary. This provides evidence that the g-theorem of (1 + 1)-dimensional field theories generalizes to higher dimensions.

“…In Lorentzian signature, this breaks the global symmetry group from SO(d, 2) to SO(d − 1, 2) [28]. Since SO(d − 1, 2) is the isometry group of AdS d , the natural semiclassical dual M d+1 is the Janus metric, where we foliate the bulk with warped copies of AdS d [29,30]:…”

Section: Ads/bcftmentioning

confidence: 99%

“…Pure AdS d+1 has warp factor f AdS (µ) := L AdS sin −1 (µ), so the metric has denominator Z 2 [30]. To recover the usual AdS/CFT correspondence far from the boundary, the warp factor f must approach f AdS as µ → 0.…”

Section: Ads/bcftmentioning

confidence: 99%

Brane dynamics from the first law of entanglement

Cooper

Neuenfeld

Rozali

et al. 2020

In this note, we study the first law of entanglement in a boundary conformal field theory (BCFT) dual to warped AdS cut off by a brane. Exploiting the symmetry of boundary-centered half-balls in the BCFT, and using Wald's covariant phase space formalism in the presence of boundaries, we derive constraints from the first law for a broad range of covariant bulk Lagrangians. We explicitly evaluate these constraints for Einstein gravity, and find a local equation on the brane which is precisely the Neumann condition of Takayanagi [arXiv:1105.5165] at linear order in metric perturbations. This is analogous to the derivation of Einstein's equations from the first law of entanglement entropy. This machinery should generalize to give local linearized equations of motion for higher-derivative bulk gravity with additional fields. arXiv:1912.05746v1 [hep-th]