Virasoro vacuum block at next-to-leading order in the heavy-light limit

TL;DR

This paper calculates the next-to-leading order correction to the Virasoro vacuum block in the heavy-light limit, providing a more precise understanding of 4-point functions in 2D CFTs and their holographic duals.

Contribution

It presents the first closed-form computation of the quadratic correction to the vacuum Virasoro block at large central charge for generic heavy operator ratios.

Findings

Derived the quadratic correction term in the semiclassical Virasoro block.

Extended the match between CFT calculations and AdS_3 gravity beyond leading order.

Potentially improves the precision of holographic entanglement entropy calculations.

Abstract

We consider the semiclassical limit of the vacuum Virasoro block describing the diagonal 4-point correlation functions on the sphere. At large central charge c, after exponentiation, it depends on two fixed ratios h_H/c and h_L/c, where h_{H, L} are the conformal dimensions of the 4-point function operators. The semiclassical block may be expanded in powers of the light ratio h_L/c and the leading non-trivial (linear) order is known in closed form as a function of h_H/c. Recently, this contribution has been matched against AdS_3 gravity calculations where heavy operators build up a classical geometry corresponding to a BTZ black hole, while the light operators are described by a geodesic in this background. Here, we compute for the first time the next-to-leading quadratic correction O((h_L/c)^{2}), again in closed form for generic heavy operator ratio h_H/c. The result is a highly non-trivial extension of the leading order and may be relevant for further refined AdS_{3}/CFT_{2} tests. Applications to the two-interval R\'enyi entropy are also presented.