We study thermal two-point functions and four-point functions involving two heavy twisted operators and two light probes in symmetric product orbifolds. We identify cases where they are universal at large $\textit{N}$, that is, they are only sensitive to the orbifold structure. Surprisingly, such observables mimic correlators obtained from the BTZ background, even though symmetric product orbifolds are not dual to semi-classical gravity. We discuss the interpretation of these results in light of the criteria for emergence of spacetime via Von Neumann algebras. Our analysis implies that a condition on the infinite $\textit{N}$ thermal two-point functions cannot be stringent enough to define an emergent spacetime and the concept of a sharp horizon.

Italy

Alexandre Belin

United States

Switzerland

Suzanne Bintanja

United Kingdom

Alejandra Castro

Waltraut Knop

Symmetric product orbifold universality and the mirage of an emergent spacetime

We consider an effective theory of massive scalar fields on a fixed AdS d+1 background with a cubic extremal interaction among them. A bulk coupling is called extremal whenever the corresponding conformal dimension of any of the dual CFT d  operators matches the sum of all the others. For cubic bulk couplings, this is ∆ i  + ∆ j  = ∆ k . These bulk interactions are often disregarded in the literature since they do not appear in traditional models of AdS/CFT. Turning them on yields a divergent vertex in the dual CFT, and here we show that these divergences can be regulated. Once renormalized, we demonstrate that this coupling introduces non-trivial mixing between single- and double-trace operators, and we compute the anomalous dimensions of the corrected operators to leading order in perturbation theory.

Argentina

Pedro Martinez

Revisiting extremal couplings in AdS/CFT

We quantify how constraints on light states affect the asymptotic growth of heavy states in weak Jacobi forms. The constraints we consider are sparseness conditions on the Fourier coefficients of these forms, which are necessary to interpret them as gravitational path integrals. Using crossing kernels, we extract the leading and subleading behavior of these coefficients and show that the leading Cardy-like growth is robust in a wide regime of validity. On the other hand, we find that subleading corrections are sensitive to the constraints placed on the light states, and we quantify their imprint on the asymptotic growth of states. Our approach is tested against the generating function of symmetric product orbifolds, where we provide new insights into the factors contributing to the asymptotic growth of their Fourier coefficients. Finally, we use our methods to revisit the UV/IR connection that relates black hole microstate counting to modular forms. We provide a microscopic interpretation of the logarithmic corrections to the entropy of BPS black holes in   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2, 4 ungauged supergravity in four and five dimensions, and tie it to consistency conditions in AdS3/CFT2.

China

Luis Apolo

Netherlands

Diego Liska

The light we can see: extracting black holes from weak Jacobi forms

A correction to this paper has been published: https://doi.org/10.1007/JHEP07(2023)120

Japan

Ioana Coman

Jackson Fliss

Claire Zukowski

Erratum to: Keeping matter in the loop in dS3 quantum gravity

We propose a mechanism that couples matter fields to three-dimensional quantum gravity, which can be used for theories with a positive or negative cosmological constant. Our proposal is rooted in the Chern-Simons formulation of three-dimensional gravity and makes use of the Wilson spool, a collection of Wilson loops winding around closed paths of the background. We show that the Wilson spool correctly reproduces the one-loop determinant of a free massive scalar field on rotating black holes in <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math> and Euclidean <math><mrow><msub><mrow><mi>dS</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math> as <math><msub><mi>G</mi><mi>N</mi></msub><mo>→</mo><mn>0</mn></math>. Moreover, we describe how to incorporate quantum metric fluctuations into this formalism.

Jackson R. Fliss

Coupling Fields to 3D Quantum Gravity via Chern-Simons Theory

A holographic conformal field theory is dual to semiclassical general relativity in anti–de Sitter space coupled to matter fields. If the conformal field theory (CFT) factorizes in the large-<math><mrow><mi>N</mi></mrow></math> limit, then all couplings in its dual are suppressed by the Planck scale, making the matter fields weakly interacting. We propose a mechanism to produce CFTs whose dual matter fields couple weakly to gravity, but interact strongly with each other. We achieve this by turning on exactly marginal multitrace deformations, and quantify the effect using conformal perturbation theory.

Christoph A. Keller

Conformal field theories dual to quantum gravity with strongly coupled matter

We analyze the thermodynamic response near extremality of charged black holes in four-dimensional Einstein-Maxwell theory with a positive cosmological constant. The latter exhibit three different extremal limits, dubbed cold, Nariai and ultracold configurations, with near-horizon geometries AdS2 × S 2, dS2 × S 2, Mink2 × S 2, respectively. For each of these three cases we analyze small deformations away from extremality, and contrast their response. We also construct the effective two-dimensional theory, obtained by dimensional reduction, that captures these features and provide a more detailed analysis of the perturbations around the near-horizon geometry for each case. Our results for the ultracold case in particular show an interesting interplay between the entropy variation and charge variation, realizing a different response in comparison to the other two near-extremal limits.

Belgium

Francesca Mariani

Chiara Toldo

Near-extremal limits of de Sitter black holes

We propose a mechanism that couples matter fields to three-dimensional de Sitter quantum gravity. Our construction is based on the Chern-Simons formulation of three-dimensional Euclidean gravity, and it centers on a collection of Wilson loops winding around Euclidean de Sitter space. We coin this object a Wilson spool. To construct the spool, we build novel representations of 𝔰𝔲(2). To evaluate the spool, we adapt and exploit several known exact results in Chern-Simons theory. Our proposal correctly reproduces the one-loop determinant of a free massive scalar field on S 3 as G  N  → 0. Moreover, allowing for quantum metric fluctuations, it can be systematically evaluated to any order in perturbation theory.

Keeping matter in the loop in dS3 quantum gravity

Symmetric product orbifold theories are valuable due to their universal features at large N. Here we will demonstrate that they have features that are not as pervasive: we provide evidence of strange behaviour under deformations within their moduli space. To this end, we consider the symmetric product orbifold of tensor products of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 super-Virasoro minimal models, and classify them according to two criteria. The first criterion is the existence of a single-trace twisted exactly marginal operator that triggers the deformation. The second criterion is a sparseness condition on the growth of light states in the elliptic genera. In this context we encounter a strange variety: theories that obey the first criterion but the second criterion falls into a Hagedorn-like growth. We explain why this may be counter-intuitive and discuss how it might be accounted for in conformal perturbation theory. We also find a new infinite class of theories that obey both criteria, which are necessary conditions for each moduli space to contain a supergravity point.

Nathan Benjamin

Jildou Hollander

The stranger things of symmetric product orbifold CFTs

We analyze how deforming symmetric product orbifolds of two-dimensional   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 conformal field theories by an exactly marginal operator lifts higher spin currents present at the orbifold point. We find on the one hand that these currents are universally lifted regardless of the underlying CFT. On the other hand the details of the lifting are surprisingly non-universal, with dependence on the central charge of the underlying CFT and the specific marginal operator in use. In the context of the AdS/CFT correspondence, our results illustrate the mechanism by which the stringy spectrum turns into a supergravity spectrum when moving through the moduli space. They also provide further evidence that symmetric product orbifolds of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 2 minimal models are holographic.