Holographic Construction of Excited CFT States

TL;DR

This paper develops a systematic holographic method to construct bulk solutions dual to excited states in conformal field theories, emphasizing a perturbative approach that captures universal features and matches CFT calculations.

Contribution

It introduces a perturbative holographic construction for excited CFT states, highlighting the universal linearized solution and detailed higher-order corrections based on operator properties.

Findings

Universal linearized bulk solutions depend only on operator conformal dimension.

Exact agreement between CFT and bulk 1-point functions for 2D states.

Higher-order bulk solutions incorporate detailed operator interactions.

Abstract

We present a systematic construction of bulk solutions that are dual to CFT excited states. The bulk solution is constructed perturbatively in bulk fields. The linearised solution is universal and depends only on the conformal dimension of the primary operator that is associated with the state via the operator-state correspondence, while higher order terms depend on detailed properties of the operator, such as its OPE with itself and generally involve many bulk fields. We illustrate the discussion with the holographic construction of the universal part of the solution for states of two dimensional CFTs, either on $R \times S^1$ or on $R^{1,1}$. We compute the 1-point function both in the CFT and in the bulk, finding exact agreement. We comment on the relation with other reconstruction approaches.