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.
Highlights
This was studied in general in [1] for the case of the 2-point function, finding an elegant expansion in terms of Gegenbauer polynomials, whose coefficients incorporate both the OPE data as well as the non-zero vacuum expectation values in the thermal background
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
Summary
We are interested on thermal correlation functions of scalar operators in holographic ddimensional CFT’s. We will mostly focus on the case where operators are inserted at the same spatial point, which, with no loss of generality can be taken to be 0, that is, we will consider xi = (ti, 0). The finite temperature state is dual to a black brane in AdSd+1. Each operator is dual to a fluctuating scalar field φi in the black brane in AdSd+1 with its mass related by the standard holographic formula to the dimension of the dual operator, d ∆= +. We shall consider operators of large scaling dimensions. For such operators, ∆ ≈ mR when mR 1. The bulk lagrangian is obtained by expanding the corresponding gravitational action in the fluctuations, where terms higher-than-quadratic in the fluctuations — suppressed by
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