Thermalization in Large-N CFTs

Abstract

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. Unlike multi stress tensors, these light operators violate the Eigenstate Thermalization Hypothesis and do not thermalize.

arXiv comment67 pages. 6 figures. v2: References added. v3: Minor corrections

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• Gravitational orbits, double-twist mirage, and many-body scars
• Black hole perturbation theory and multiple polylogarithms
• Thermal Stress Tensor Correlators, OPE and Holography
• Photon emission from an excited string
• An embedding formalism for CFTs in general states on curved backgrounds
• Freedom near Lightcone and ANEC Saturation
• Conformal line defects at finite temperature
• Bananas are Unparticles: Differential Equations and Cosmological Bootstrap
• Approximate Symmetries in $d=4$ CFTs with an Einstein Gravity Dual
• Toward Null State Equations in $d>2$
• A Strategy for Proving the Strong Eigenstate Thermalization Hypothesis : Chaotic Systems and Holography
• Universal thermalization dynamics in (1+1)d QFTs