Thermalization in Large-N CFTs

Understand

In d-dimensional CFTs with a large number of degrees of freedom an important set of operators consists of the stress tensor and its products, multi stress tensors.

• Thermalization of such operators, the equality between their expectation values in heavy states and at finite temperature, is equivalent to a universal behavior of their OPE coefficients with a pair of identical heavy operators.
• We verify this behavior in a number of examples which include holographic and free CFTs and provide a bootstrap argument for the general case.
• In a free CFT we check the thermalization of multi stress tensor operators directly and also confirm the equality between the contributions of multi stress tensors to heavy-heavy-light-light correlators and to the corresponding thermal light-light two-point functions by disentangling the contributions of other light operators.