Holographic thermal correlators revisited

Abstract

We study 2-point correlation functions for scalar operators in position space through holography including bulk cubic couplings as well as higher curvature couplings to the square of the Weyl tensor. We focus on scalar operators with large conformal dimensions. This allows us to use the geodesic approximation for propagators. In addition to the leading order contribution, captured by geodesics anchored at the insertion points of the operators on the boundary and probing the bulk geometry thoroughly studied in the literature, the first correction is given by a Witten diagram involving both the bulk cubic coupling and the higher curvature couplings. As a result, this correction is proportional to the VEV of a neutral operator $O_k$ and thus probes the interior of the black hole exactly as in the case studied by Grinberg and Maldacena [13]. The form of the correction matches the general expectations in CFT and allows to identify the contributions of $T^n{O}_k$ (being $T^n$ the general contraction of n energy-momentum tensors) to the 2-point function. This correction is actually the leading term for off-diagonal correlators (i.e. correlators for operators of different conformal dimension), which can then be computed holographically in this way.

arXiv comment23 pages

References in corpus (19)

• Three-Point Functions of Chiral Operators in D=4, $\mathcal{N}=4$ SYM at Large N
• Coupling Constant Dependence in the Thermodynamics of N=4 Supersymmetric Yang-Mills Theory
• The Black Hole Singularity in AdS/CFT
• Extremal surfaces as bulk probes in AdS/CFT
• Excursions beyond the horizon: Black hole singularities in Yang-Mills theories (I)
• The Conformal Bootstrap at Finite Temperature
• A Cardy Formula for Three-Point Coefficients: How the Black Hole Got its Spots
• AdS_5 x S^5 Black Hole Metric at O(alpha'^3)
• Bulk-cone singularities & signatures of horizon formation in AdS/CFT
• Proper time to the black hole singularity from thermal one-point functions
• Universal Lowest-Twist in CFTs from Holography
• Correlation functions in finite temperature CFT and black hole singularities
• Probing Universalities in d>2 CFTs: from Black Holes to Shockwaves
• Holographic Correlators at Finite Temperature
• Singularities of thermal correlators at strong coupling
• AdS black holes as reflecting cavities
• Thermal correlation functions in CFT and factorization
• Tidal excitation as mixing in thermal CFT
• Time singularities of correlators from Dirichlet conditions in AdS/CFT

Cited by in corpus (3)

• Thermal Stress Tensor Correlators, OPE and Holography
• Freedom near Lightcone and ANEC Saturation
• Approximate Symmetries in $d=4$ CFTs with an Einstein Gravity Dual