Three Point Functions in Higher Spin AdS3 Holography with 1/N Corrections

Abstract

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.

Conformal blocks from Wilson lines with loop corrections

“…, N . In this paper, we adopt the convention for the higher spin currents in [10,21]. In particular, the two point functions are given by…”

“…where the expressions of k a , k b , k c may be used as in (A.11) of [21]. Here, z 2 2 F 1 (2, 2; 4; z) at the 1/c order corresponds to the global block 3 with the exchange of the energy momentum tensor.…”

“…In appendix A, we summarize CFT computations of four point conformal blocks in the W N minimal model. In particular, we obtain four point function of (1.4) with Λ corresponding a rectangular Young diagram and Ξ = f. As an application of [10,21], we compute the 1/c corrections of higher spin charges for the scalar operators using the method of conformal block decomposition. In appendix B, we include some technical details of sl(3) Lie algebras.…”

Superconformal blocks from Wilson lines with loop corrections

“…These superconformal blocks should be useful as fundamental objects for the study of superstring theory and AdS/CFT correspondence. Furthermore, we could read off higher spin charges in the N = 2 W N +1 minimal model by using the N = 2 superconformal blocks as in [58]. It might be rather easier to use the N = 1 superconformal blocks obtained here in the N = 1 higher spin holographies of [59,60].…”

Quantum correction to chaos in Schwarzian theory

“…Note that there has been a series of works to pursue a similar question[29][30][31]. Also, see[32][33][34].…”