Thermal correlation functions in CFT and factorization

Abstract

We study 2-point and 3-point functions in CFT at finite temperature for large dimension operators using holography. The 2-point function leads to a universal formula for the holographic free energy in $d$ dimensions in terms of the $c$-anomaly coefficient. By including ${\alpha }^{\prime }$ corrections to the black brane background, one can reproduce the leading correction at strong coupling. In turn, 3-point functions have a very intricate structure, exhibiting a number of interesting properties. In simple cases, we find an analytic formula, which reduces to the expected expressions in different limits. When the dimensions satisfy ${\Delta }_i={\Delta }_j+{\Delta }_k$, the thermal 3-point function satisfies a factorization property. We argue that in $d>2$ factorization is a reflection of the semiclassical regime.

26 pages

References in corpus (6)

• Krylov complexity in conformal field theory
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• Proper time to the black hole singularity from thermal one-point functions
• Correlation functions in finite temperature CFT and black hole singularities
• Black holes and universality classes of critical points
• Finite-temperature three-point function in 2D CFT

Cited by in corpus (7)

• Thermal Stress Tensor Correlators, OPE and Holography
• Exact thermal correlators of holographic $CFT$s
• Thermal three-point functions from holographic Schwinger-Keldysh contours
• Holographic thermal correlators revisited
• Freedom near Lightcone and ANEC Saturation
• Approximate Symmetries in $d=4$ CFTs with an Einstein Gravity Dual
• Holographic thermal propagator for arbitrary scale dimensions