Comments on a state-operator correspondence for the torus

Belin, Alexandre; Kruthoff, Jorrit

doi:10.21468/scipostphys.5.6.060

Cited by 18 publications

(11 citation statements)

References 24 publications

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“…can also be multiple one-point structures on T n for n ≥ 2, so there is more data to compute. For recent work on CFTs on spatial tori, see [94,95].…”

Section: Discussionmentioning

confidence: 99%

The conformal bootstrap at finite temperature

Iliesiu

Kologlu

Mahajan

et al. 2018

J. High Energ. Phys.

106

158

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We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one-and two-point functions of local operators on the plane. The KMS condition for thermal two-point functions is cast as a crossing equation. By studying the analyticity properties of thermal two-point functions, we derive a "thermal inversion formula" whose output is the set of thermal one-point functions for all operators appearing in a given OPE. This involves identifying a kinematic regime which is the analog of the Regge regime for four-point functions. We demonstrate the effectiveness of the inversion formula by recovering the spectrum and thermal one-point functions in mean field theory, and computing thermal onepoint functions for all higher-spin currents in the critical O(N ) model at leading order in 1/N . Furthermore, we develop a systematic perturbation theory for thermal data in the large spin, low-twist spectrum of any CFT. We explain how the inversion formula and KMS condition may be combined to algorithmically constrain CFTs at finite temperature. Throughout, we draw analogies to the bootstrap for vacuum four-point functions. Finally, we discuss future directions for the thermal conformal bootstrap program, emphasizing applications to various types of CFTs, including those with holographic duals.

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“…can also be multiple one-point structures on T n for n ≥ 2, so there is more data to compute. For recent work on CFTs on spatial tori, see [94,95].…”

Section: Discussionmentioning

confidence: 99%

The conformal bootstrap at finite temperature

Iliesiu

Kologlu

Mahajan

et al. 2018

J. High Energ. Phys.

106

158

View full text Add to dashboard Cite

show abstract

“…This means that the conformal transformation properties of the states and operators considered here will not be related in a nice way, which is why such a correspondence is usually not considered. See[183] for more discussion on this. For our purposes this does not matter, since we only care about transformations under p-form global symmetries and these will be the same.…”

mentioning

confidence: 99%

Symmetries in Quantum Field Theory and Quantum Gravity

Harlow

Ooguri

2021

Commun. Math. Phys.

276

302

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In this paper we use the AdS/CFT correspondence to refine and then establish a set of old conjectures about symmetries in quantum gravity. We first show that any global symmetry, discrete or continuous, in a bulk quantum gravity theory with a CFT dual would lead to an inconsistency in that CFT, and thus that there are no bulk global symmetries in AdS/CFT. We then argue that any "long-range" bulk gauge symmetry leads to a global symmetry in the boundary CFT, whose consistency requires the existence of bulk dynamical objects which transform in all finite-dimensional irreducible representations of the bulk gauge group. We mostly assume that all internal symmetry groups are compact, but we also give a general condition on CFTs, which we expect to be true quite broadly, which implies this. We extend all of these results to the case of higher-form symmetries. Finally we extend a recently proposed new motivation for the weak gravity conjecture to more general gauge groups, reproducing the "convex hull condition" of Cheung and Remmen.An essential point, which we dwell on at length, is precisely defining what we mean by gauge and global symmetries in the bulk and boundary. Quantum field theory results we meet while assembling the necessary tools include continuous global symmetries without Noether currents, new perspectives on spontaneous symmetry-breaking and 't Hooft anomalies, a new order parameter for confinement which works in the presence of fundamental quarks, a Hamiltonian lattice formulation of gauge theories with arbitrary discrete gauge groups, an extension of the Coleman-Mandula theorem to discrete symmetries, and an improved explanation of the decay π 0 → γγ in the standard model of particle physics. We also describe new black hole solutions of the Einstein equation in d + 1 dimensions with horizon topology T p × S d−p−1 .

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“…Some examples of when this is not the case are the TFD state below the Hawking-Page transition or the AdS soliton[33,34].…”

mentioning

confidence: 99%

Complexity and the bulk volume, a new York time story

Belin

Lewkowycz

Sárosi

2019

J. High Energ. Phys.

Self Cite

121

172

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We study the boundary description of the volume of maximal Cauchy slices using the recently derived equivalence between bulk and boundary symplectic forms. The volume of constant mean curvature slices is known to be canonically conjugate to "York time". We use this to construct the boundary deformation that is conjugate to the volume in a handful of examples, such as empty AdS, a backreacting scalar condensate, or the thermofield double at infinite time. We propose a possible natural boundary interpretation for this deformation and use it to motivate a concrete version of the complexity=volume conjecture, where the boundary complexity is defined as the energy of geodesics in the Kähler geometry of half sided sources. We check this conjecture for Bañados geometries and a mini-superspace version of the thermofield double state. Finally, we show that the precise dual of the quantum information metric for marginal scalars is given by a particularly simple symplectic flux, instead of the volume as previously conjectured.Here, we are denoting linearized deformations by |δΨ λ ≈ |Ψ λ+δλ − |Ψ λ , the bulk field φ is dual to the operator sourced by λ, its conjugate momentum is π, and Σ is a bulk initial value surface. This is the main result of [21] and it gives a

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Comments on a state-operator correspondence for the torus

Cited by 18 publications

References 24 publications

The conformal bootstrap at finite temperature

The conformal bootstrap at finite temperature

Symmetries in Quantum Field Theory and Quantum Gravity

Complexity and the bulk volume, a new York time story

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