Jan Boruch

We develop a nonperturbative definition of RMT 2 : a generalization of random matrix theory that is compatible with the symmetries of two-dimensional conformal field theory. Given any random matrix ensemble, its n -point spectral correlations admit a prescribed modular-invariant lift to RMT 2 , which moreover reduce to the original random matrix correlators in a near-extremal limit. Central to the prescription is a presentation of random matrix theory in Mellin space, which lifts to two dimensions via the SL ( 2 , Z ) spectral decomposition employed in previous work. As a demonstration we perform the explicit RMT 2 lift of two-point correlations of the GUE Airy model. We propose that in AdS 3 pure gravity, semiclassical amplitudes for off-shell n -boundary torus wormholes with topology Σ 0 , n × S 1 are given by the RMT 2 lift of JT gravity wormhole amplitudes. For the three-boundary case, we identify a gravity calculation which matches the RMT 2 result.

The supersymmetric index of 5d black strings and spinning black holes in M-theory is related to that of 4d black holes in type IIA supergravity when both theories are compactified on the same Calabi-Yau threefold. We find the finite-temperature saddles for the 5d gravitational supersymmetric index by uplifting the recently found attractor saddles of the corresponding 4d index. We study uplifts for two types of geometries: 5d black holes and 5d black strings. For 5d black holes, the uplift guarantees that the index of 4d and 5d black holes match. For 5d black strings, the saddle reproduces the microscopic index at leading order in G _N , even without the conventional decoupling limit taken in AdS/CFT. In particular, when the temperature is set to be finite in the 5d flat space region, the black string index is computed from an asymptotically flat solution where the AdS throat is absent. Further, as the temperature is lowered and eventually becomes infinitesimally small in the flat space region, the solution admits a novel decoupling limit in which the AdS₃ throat takes the form of a finite-temperature BTZ black hole that is known to compute the index in AdS₃/CFT₂. This represents the first step towards understanding holography for supersymmetric observables in flat space, away from the decoupling limit.

In AdS/CFT, two-sided black holes are described by states in the tensor product of two Hilbert spaces associated with the two asymptotic boundaries of the spacetime. Understanding how such a tensor product arises from the bulk perspective is an important open problem in holography, known as the factorisation puzzle. In this paper, we show how the Hilbert space of bulk states factorises due to non-perturbative contributions of spacetime wormholes: the trace over two-sided states with different particle excitations behind the horizon factorises into a product of traces of the left and right sides. This precisely occurs when such states form a complete basis for the bulk Hilbert space. We prove that the factorisation of the trace persists to all non-perturbative orders in 1/G _N , consequently providing a possible resolution to the factorisation puzzle from the gravitational path integral. In the language of von Neumann algebras, our results provide strong evidence that the algebra of one-sided observables transitions from a Type II or Type III algebra, depending on whether or not perturbative gravity effects are included, to a Type I factor when including non-perturbative corrections in the bulk.

Understanding how to prepare and count black hole micro-states by using the gravitational path integral is one of the most important problems in quantum gravity. Nevertheless, a state-by-state count of black hole microstates is difficult because the apparent number of degrees of freedom available in the gravitational effective theory can vastly exceed the entropy of the black hole, even in the special case of BPS black holes. In this paper, we show that we can use the gravitational path integral to prepare a basis for the Hilbert space of all BPS black hole microstates. We find that the dimension of this Hilbert space computed by an explicit state count is in complete agreement with the degeneracy obtained from the Gibbons-Hawking prescription. Specifically, this match includes all non-perturbative corrections in 1/G _N . Such corrections are, in turn, necessary in order for this degeneracy of BPS states to match the non-perturbative terms in the 1/G _N expansion in the string theory count of such microstates.

A correction to this paper has been published: https://doi.org/10.1007/JHEP07(2021)016

In this work we elaborate on holographic description of the path-integral optimization in conformal field theories (CFT) using Hartle-Hawking wave functions in Anti-de Sitter spacetimes. We argue that the maximization of the Hartle-Hawking wave function is equivalent to the path-integral optimization procedure in CFT. In particular, we show that metrics that maximize gravity wave functions computed in particular holographic geometries, precisely match those derived in the path-integral optimization procedure for their dual CFT states. The present work is a detailed version of [1] and contains many new results such as analysis of excited states in various dimensions including JT gravity, and a new way of estimating holographic path-integral complexity from Hartle-Hawking wave functions. Finally, we generalize the analysis to Lorentzian Anti-de Sitter and de Sitter geometries and use it to shed light on path-integral optimization in Lorentzian CFTs.

We propose a gravity dual description of the path integral optimization in conformal field theories [Caputa et al., Phys. Rev. Lett. 119, 071602 (2017)], using Hartle-Hawking wave functions in anti–de Sitter spacetime. We show that the maximization of the Hartle-Hawking wave function is equivalent to the path integral optimization procedure. Namely, the variation of the wave function leads to a constraint, equivalent to the Neumann boundary condition on a bulk slice, whose classical solutions reproduce metrics from the path integral optimization in conformal field theories. After taking the boundary limit of the semiclassical Hartle-Hawking wave function, we reproduce the path integral complexity action in two dimensions, as well as its higher- and lower-dimensional generalizations. We also discuss an emergence of holographic time from conformal field theory path integrals.