Harmonic analysis of 2d CFT partition functions

Benjamin, Nathan; Collier, Scott; Fitzpatrick, A. Liam; Maloney, Alexander; Perlmutter, Eric

doi:10.1007/jhep09(2021)174

Cited by 45 publications

(51 citation statements)

References 68 publications

(150 reference statements)

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“…dualities between ensembles of boundary systems and bulk gravitational ones [228][229][230][231][232][233]? What lessons can be drawn from thinking about these questions from the perspective of the Hilbert space of baby universes [128,129,161,[234][235][236]?…”

Section: Fine Structure Of Black Holesmentioning

confidence: 99%

Snowmass White Paper: Quantum Aspects of Black Holes and the Emergence of Spacetime

Bousso¹,

Dong²,

Engelhardt³

et al. 2022

Preprint

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Black holes provide a window into the microscopic structure of spacetime in quantum gravity. Recently the quantum information contained in Hawking radiation has been calculated, verifying a key aspect of the consistency of black hole evaporation with quantum mechanical unitarity.This calculation relied crucially on recent progress in understanding the emergence of bulk spacetime from a boundary holographic description. Spacetime wormholes have played an important role in understanding the underpinnings of this result, and the precision study of such wormholes, in this and other contexts, has been enabled by the development of low-dimensional models of holography.In this white paper we review these developments and describe some of the deep open questions in this subject. These include the nature of the black hole interior, potential applications to quantum cosmology, the gravitational explanation of the fine structure of black holes, and the development of further connections to quantum information and laboratory quantum simulation.

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Section: Fine Structure Of Black Holesmentioning

confidence: 99%

Snowmass White Paper: Quantum Aspects of Black Holes and the Emergence of Spacetime

Bousso¹,

Dong²,

Engelhardt³

et al. 2022

Preprint

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“…See e.g. [227] for a sampling of the relevant mathematics, and [207,228] for recent discussions in the context of the bootstrap. Can a wider array of mathematical tools be applied to conformal field theory, and vice-versa?…”

Section: Averaging and Randomnessmentioning

confidence: 99%

Snowmass White Paper: The Analytic Conformal Bootstrap

Hartman¹,

Mazáč²,

Simmons-Duffin³

et al. 2022

Preprint

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The analytic conformal bootstrap is an array of techniques to characterize, constrain, and solve strongly interacting quantum field theories using symmetries, causality, unitarity, and other general principles. In the last decade, bolstered by the development of new Lorentzian methods, it has been used to solve conformal field theories at large spin; to place bounds on energy distributions, event shapes, operator product coefficients, and other observables; and to understand aspects of quantum gravity in anti-de Sitter space. We review these advances and highlight several promising areas for future exploration. Targets include developing new methods to close the gap between numerical and analytic bounds, extending the bootstrap beyond conformal fixed points, applications to quantum gravity and cosmology, and building on ties to condensed matter theory and mathematics.

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“…Furthermore, it is shown [12,35] that JT gravity is dual to a matrix ensemble. Later on more explicit 2d [12,[36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52] and 3d [53][54][55][56][57][58][59][60][61][62][63][64] examples of ensemble duality are proposed. See further explorations of wormhole, baby universe and ensemble average in [9,.…”

Section: Introductionmentioning

confidence: 99%

Baby universes, ensemble averages and factorizations with matters

Peng

Tian

2021

Preprint

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We investigate 2D topological gravity theories with matter fields turned on. We compute correlators of boundary creation operators with extra matter insertions. We provide a systematic procedure to determine a set of α-states on which the correlation functions of the different boundary operators factorize. Our results suggest that the boundary dual is an ensemble average of theories with different numbers of replicas of a seed matter contribution that is represented by excitations on top of the gravity sector. The construction of the α-states and the subsequent computations in the Hilbert space point of view are most conveniently done when the bulk couplings of the matter fields are expanded in a basis of vortices, which can be thought of as a 1-dimensional analogue of the SD-branes. We further demonstrate the existence of null states and the conditions imposed by reflection positivity. Moreover, in the CGS model with only disk and cylinder topologies we map the baby universe creation and annihilation operators to the coupling constants in the one time SYK model, which allows us to match the wormhole and half-wormhole contributions in the CGS model explicitly to those identified in the SYK model. This explicitly realizes Coleman's initial idea. Some details of the computations in a variety of concrete models are presented.

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Harmonic analysis of 2d CFT partition functions

Cited by 45 publications

References 68 publications

Snowmass White Paper: Quantum Aspects of Black Holes and the Emergence of Spacetime

Snowmass White Paper: Quantum Aspects of Black Holes and the Emergence of Spacetime

Snowmass White Paper: The Analytic Conformal Bootstrap

Baby universes, ensemble averages and factorizations with matters

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