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.

arXiv comment26 pages

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Cited by in corpus (7)

• Thermal Stress Tensor Correlators, OPE and Holography
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• 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