Three point functions in higher spin AdS_3 holography with 1/N corrections

TL;DR

This paper computes three-point functions involving scalar operators and higher spin currents in 2d W_N minimal models, incorporating 1/N quantum corrections to test the holographic duality with higher spin gravity.

Contribution

It introduces a systematic method to calculate 3-point functions with 1/N corrections in 2d W_N models, extending previous leading-order results and confirming conjectured relations.

Findings

Reproduced known leading-order three-point functions

Derived new results at next-to-leading order in 1/N

Confirmed consistency with previously conjectured relations

Abstract

We examine three point functions with two scalar operators and a higher spin current in 2d W_N minimal model to the next non-trivial order in 1/N expansion. The minimal model was proposed to be dual to a 3d higher spin gauge theory, and 1/N corrections should be interpreted as quantum effects in the dual gravity theory. We develop a simple and systematic method to obtain three point functions by decomposing four point functions of scalar operators with Virasoro conformal blocks. Applying the method, we reproduce known results at the leading order in 1/N and obtain new ones at the next leading order. As confirmation, we check that our results satisfy relations among three point functions conjectured before.