Structure Constants from Modularity in Warped CFT

Abstract

We derive a universal formula for the asymptotic growth of the mean value of three-point coefficient for Warped Conformal Field Theories (WCFTs), and provide a holographic calculation in BTZ black holes. WCFTs are two dimensional quantum field theories featuring a chiral Virasoro and U(1) Kac-Moody algebra, and are conjectured to be holographically dual to quantum gravity on asymptotically AdS${}_3$ spacetime with Comp$\grave{\mathrm{e}}$re-Song-Strominger boundary conditions. The WCFT calculation amounts to the calculation of one-point functions on torus, whose high temperature limit can be approximated by using modular covariance of WCFT, similar to the derivation of Cardy formula. The bulk process is given by a tadpole diagram, with a massive spinning particle propagates from the infinity to the horizon, and splits into particle and antiparticle which annihilate after going around the horizon of BTZ black holes. The agreement between the bulk and WCFT calculations indicates that the black hole geometries in asymptotically AdS${}_3$ spacetimes can emerge upon coarse-graining over microstates in WCFTs, similar to the results of Kraus and Maloney in the context of AdS/CFT[arXiv:1608.03284].

24 pages, 1 figure

References in corpus (11)

• Warped AdS_3 Black Holes
• Semi-classical central charge in topologically massive gravity
• Boundary conditions for spacelike and timelike warped AdS_3 spaces in topologically massive gravity
• Warped Conformal Field Theory as Lower Spin Gravity
• Holographic entanglement entropy and gravitational anomalies
• Charged structure constants from modularity
• Tweaking one-loop determinants in AdS${}_3$
• Microscopic Realization of the Kerr/CFT Correspondence
• Witten Diagrams for Torus Conformal Blocks
• Two Virasoro symmetries in stringy warped AdS${}_3$
• Entanglement and chaos in warped conformal field theories

Cited by in corpus (14)

• Universal Dynamics of Heavy Operators in CFT${}_2$
• Warped Symmetries of the Kerr Black Hole
• Modular Hamiltonians in flat holography and (W)AdS/WCFT
• 2d Galilean Field Theories with Anisotropic Scaling
• Complexity of warped conformal field theory
• Reflected Entropy in AdS${}_3$/WCFT
• Holographic entanglement entropy in AdS${}_3$$/$WCFT
• Supersymmetric Warped Conformal Field Theory
• Holographic Dual of Conformal Field Theories with Very Special $T\bar{J}$ Deformations
• BMS Modular Diaries: Torus one-point function
• Warped Conformal Symmetries of the Accelerating Kerr Black Hole
• Gravitational radiations of Kerr black hole from warped symmetries
• Crossing, Modular Averages and $N\leftrightarrow k$ in WZW Models
• Warped CFT duals of the Plebański-Demiański family of solutions