Holographic relations for OPE blocks in excited states

TL;DR

This paper explores the holographic duality between boundary OPE blocks and bulk fields in excited AdS$_3$ geometries, analyzing how non-minimal geodesics influence this relationship.

Contribution

It introduces a decomposition of OPE blocks into quotient-invariant operators and proposes a duality with bulk fields integrated over all geodesics, including non-minimal ones.

Findings

Decomposition of OPE blocks into quotient-invariant operators

Duality with bulk fields over minimal and non-minimal geodesics

Evidence from monodromy analysis of asymptotic maps

Abstract

We study the holographic duality between boundary OPE blocks and geodesic integrated bulk fields in quotients of AdS$_3$ dual to excited CFT states. The quotient geometries exhibit non-minimal geodesics between pairs of spacelike separated boundary points which modify the OPE block duality. We decompose OPE blocks into quotient invariant operators and propose a duality with bulk fields integrated over individual geodesics, minimal or non-minimal. We provide evidence for this relationship by studying the monodromy of asymptotic maps that implement the quotients.