We study the reconstruction of the bulk operators in AdS/CFT when the geometry contains a black hole. The black hole exterior can be mapped to the CFT via a very simple Petz map which coincides with the HKLL map reconstruction of the black hole exterior. For the interior modes of the bulk theory, using the definition of the Petz recovery channel in modular theory, we can find the mapping from the black hole interior to the dual boundary theory. In the case of the evaporating black hole, it is expected that the interior modes map to some operators that have support only on the bath system, the cavity that absorbs the Hawking radiation. The most important observation that we have here is that in the case that we have a typical black hole microstate in the bulk, the CFT dual of the interior modes that we can find using the Petz recovery channel are exactly the operators that so-called “$\textit{mirror operator}$ “ in the Papadodimas-Raju proposal. Therefore, we can interpret Papadodimas-Raju proposal as an example of the Petz map reconstruction. It may help us answer some open questions about their procedure.

Italy

Niloofar Vardian

Black hole interior Petz map reconstruction and Papadodimas-Raju proposal

We study the behavior of black hole singularities across the Hawking-Page phase transitions, uncovering possible connections between the physics inside and outside the horizon. We focus on the case of spacelike singularities in Einstein-scalar theory which are of the Kasner form. We find that the Kasner exponents are continuous and non-differentiable during the second order phase transitions, while discontinuous in the first order phase transitions. We give some arguments on the universality of this behavior. We also discuss possible observables in the dual field theory which encode the Kasner exponents.

China

Yan Liu

Hong-Da Lyu

Avinash Raju

Black hole singularities across phase transitions

We study quantum chaos of rotating BTZ black holes in Topologically Massive gravity (TMG). We discuss the relationship between chaos parameters including Lyapunov exponents and butterfly velocities from shock wave calculations of out-of-time-order correlators (OTOC) and from pole-skipping analysis. We find a partial match between pole-skipping and the OTOC results in the high temperature regime. We also find that the velocity bound puts a chaos constraint on the gravitational Chern-Simons coupling.

Quantum chaos in topologically massive gravity

We use the recently developed CFT techniques of Rychkov and Tan to compute anomalous dimensions in the O( N ) Gross-Neveu model in d = 2 + ϵ dimensions. To do this, we extend the “cowpie contraction” algorithm of arXiv:1506.06616 to theories with fermions. Our results match perfectly with Feynman diagram computations.

India

ϵ -expansion in the Gross-Neveu

We define a (semi-classical) path integral for gravity with Neumann boundary conditions in D dimensions, and show how to relate this new partition function to the usual picture of Euclidean quantum gravity. We also write down the action in ADM Hamiltonian formulation and use it to reproduce the entropy of black holes and cosmological horizons. A comparison between the (background-subtracted) covariant and Hamiltonian ways of semi-classically evaluating this path integral in flat space reproduces the generalized Smarr formula and the first law. This “Neumann ensemble” perspective on gravitational thermodynamics is parallel to the canonical (Dirichlet) ensemble of Gibbons-Hawking and the microcanonical approach of Brown-York.

Chethan Krishnan

K. Kumar

An alternative path integral for quantum gravity

We quantize the space of 2-charge fuzzballs in IIB supergravity on K 3. The resulting entropy precisely matches the D1-D5 black hole entropy, including a specific numerical coefficient. A partial match (ie., a smaller coefficient) was found by Rychkov a decade ago using the Lunin-Mathur subclass of solutions — we use a simple observation to generalize his approach to the full moduli space of K 3 fuzzballs, filling a small gap in the literature.

A note on D1-D5 entropy and geometric quantization

In this note I elaborate on some features of a recent proposal of Papadodimas and Raju for a CFT description of the interior of a one-sided AdS black hole in a pure state. I clarify the treatment of 1 /N corrections, and explain how the proposal is able to avoid some of the pitfalls that have disrupted other recent ideas. I argue however that the proposal has the uncomfortable property that states in the CFT Hilbert space do not have definite physical interpretations, unlike in ordinary quantum mechanics. I also contrast the “state-dependence” of the proposal with more familiar phenomena, arguing that, unlike in quantum mechanics, the measurement process (including the apparatus) in something like the PR proposal or its earlier manifestations cannot be described by unitary evolution. These issues render the proposal somewhat ambiguous, and it seems new ideas would be needed to make some version of it work. I close with some brief speculation on to what extent quantum mechanics should hold for the experience of an infalling observer.

United States

Daniel Harlow

Aspects of the Papadodimas-Raju proposal for the black hole interior

We show that interpreting the inverse AdS 3 radius 1 /l as a Grassmann variable results in a formal map from gravity in AdS 3 to gravity in flat space. The underlying reason for this is the fact that ISO(2 , 1) is the Inonu-Wigner contraction of SO(2 , 2). We show how this works for the Chern-Simons actions, demonstrate how the general (Banados) solution in AdS 3 maps to the general flat space solution, and how the Killing vectors, charges and the Virasoro algebra in the Brown-Henneaux case map to the corresponding quantities in the BMS 3 case. Our results straightforwardly generalize to the higher spin case: the recently constructed flat space higher spin theories emerge automatically in this approach from their AdS counterparts. We conclude with a discussion of singularity resolution in the BMS gauge as an application.