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 α′ corrections to the black brane background, we 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. When the dimensions satisfy ∆ i = ∆ j + ∆ k , the thermal 3-point function satisfies a factorization property. We argue that in d > 2 factorization is a reflection of the semiclassical regime