Emergent gravity from Eguchi-Kawai reduction

Shaghoulian, Edgar

doi:10.1007/jhep03(2017)011

Cited by 18 publications

(18 citation statements)

References 102 publications

(151 reference statements)

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“…The phase transition between saddles occurs at p = k as required by modularity. This context and that of N = 4 in the last section have phase structures that can be predicted (at large k and p) using modular invariance and center symmetry arguments as explained in [35].…”

Section: N = 4 Super Yang-mills At Strong Couplingmentioning

confidence: 76%

Modular Invariance of Conformal Field Theory on S1×S3 and Circle Fibrations

Shaghoulian

2017

Phys. Rev. Lett.

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I conjecture a high-temperature-low-temperature duality for conformal field theories defined on circle fibrations like S^{3} and its lens space family. The duality is an exchange between the thermal circle and the fiber circle in the limit where both are small. The conjecture is motivated by the fact that π_{1}(S^{3}/Z_{p→∞})=Z=π_{1}(S^{1}×S^{2}) and the Gromov-Hausdorff distance between S^{3}/Z_{p→∞} and S^{1}/Z_{p→∞}×S^{2} vanishes. Several checks of the conjecture are provided: free fields, N=1 theories in four dimensions (which shows that the Di Pietro-Komargodski supersymmetric Cardy formula and its generalizations are given exactly by a supersymmetric Casimir energy), N=4 super Yang-Mills at strong coupling, and the six-dimensional N=(2,0) theory. For all examples considered, the duality is powerful enough to control the high-temperature asymptotics on the unlensed S^{3}, relating it to the Casimir energy on a highly lensed S^{3}. Such large-order quotients are more generally useful for studying quantum field theory on curved spacetimes.

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Section: N = 4 Super Yang-mills At Strong Couplingmentioning

confidence: 76%

Modular Invariance of Conformal Field Theory on S1×S3 and Circle Fibrations

Shaghoulian

2017

Phys. Rev. Lett.

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“…An intriguing aspect of the deformation considered is that it preserves center symmetry for theories where it is present. It was argued in [43] that the presence and pattern of spontaneous breaking of this symmetry is a robust way of reproducing aspects of semiclassical bulk physics when the boundary theory is placed on nontrivial topology. For example, the fact that the symmetry is unbroken means we can write correlation functions on quotient spacetimes (at leading order in N ) in terms of a sum over images of the correlation function in the original spacetime; this important property is manifest from the bulk description, and in our dual EFT is kept intact by the preservation of center symmetry along the T 2 flow.…”

Section: Entropy Densitymentioning

confidence: 99%

Holography at finite cutoff with a T2 deformation

Hartman

Kruthoff

Shaghoulian

et al. 2019

J. High Energ. Phys.

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192

290

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We generalize the T T deformation of CFT 2 to higher-dimensional large-N CFTs, and show that in holographic theories, the resulting effective field theory matches semiclassical gravity in AdS with a finite radial cutoff. We also derive the deformation dual to arbitrary bulk matter theories. Generally, the deformations involve background fields as well as CFT operators. By keeping track of these background fields along the flow, we demonstrate how to match correlation functions on the two sides in some simple examples, as well as other observables. Bulk scalar field: φBoundary value:CFT source:Bulk on-shell action:

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“…Discrete symmetries play an important role in many modern developments in quantum field theory, appearing in mixed 't Hooft anomalies , conformal field theories on nontrivial backgrounds [23][24][25][26][27][28][29], and quantum gravity [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. In this note we illustrate the conceptual and technical utility of parity symmetry in two-dimensional conformal field theory through two examples.…”

Section: Introductionmentioning

confidence: 99%

Parity and the modular bootstrap

2018

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We consider unitary, modular invariant, two-dimensional CFTs which are invariant under the parity transformation P . Combining P with modular inversion S leads to a continuous family of fixed points of the SP transformation. A particular subset of this locus of fixed points exists along the line of positive left-and right-moving temperatures satisfying β L β R = 4π 2 . We use this fixed locus to prove a conjecture of Hartman, Keller, and Stoica that the free energy of a large-c CFT 2 with a suitably sparse low-lying spectrum matches that of AdS 3 gravity at all temperatures and all angular potentials. We also use the fixed locus to generalize the modular bootstrap equations, obtaining novel constraints on the operator spectrum and providing a new proof of the statement that the twist gap is smaller than (c − 1)/12 when c > 1. At large c we show that the operator dimension of the first excited primary lies in a region in the (h, h)-plane that is significantly smaller than h + h < c/6. Our results for the free energy and constraints on the operator spectrum extend to theories without parity symmetry through the construction of an auxiliary parity-invariant partition function.

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Emergent gravity from Eguchi-Kawai reduction

Cited by 18 publications

References 102 publications

Modular Invariance of Conformal Field Theory on S1×S3 and Circle Fibrations

Modular Invariance of Conformal Field Theory on S1×S3 and Circle Fibrations

Holography at finite cutoff with a T2 deformation

Parity and the modular bootstrap

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