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Résumé |
The eigenstate thermalization hypothesis is one of the most universal features of
chaotic quantum many-body systems, which claims that matrix elements of simple
operators in high energy states has a universal structure which treats off-
diagonal elements statistically. Along with the random-matrix like behaviour of
energy eigenstates, it is one of the main smoking guns of quantum chaos. In this
talk, I will introduce the OPE randomness hypothesis: a conjecture for the
statistical distribution of OPE coefficients in chaotic conformal field theories.
This hypothesis generalizes the ETH ansatz and treats OPE coefficients
statistically, with a distribution given to leading order by a Gaussian
distribution, with corrections exponentially suppressed in the entropy. I will
give evidence for this conjecture, based on asymptotic formulas for OPE
coefficients that can be derived thanks to crossing symmetry and for 2d CFTs,
modular invariance. I will discuss the gravitational counterparts of these results
and underline the importance of Euclidean wormholes.
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