# AdS$_3$ Reconstruction with General Gravitational Dressings

## TL;DR

This paper extends the construction of AdS$_3$ proto-fields to include general gravitational dressings, analyzing gauge ambiguities, and computes quantum corrections to bulk-boundary correlators in black hole microstates.

## Contribution

It introduces a method to define bulk fields with arbitrary gravitational dressings beyond the Fefferman-Graham gauge, enhancing the understanding of gauge ambiguities in quantum gravity.

## Key findings

- Computed gravitational loop corrections to correlators in black hole microstates.
- Verified corrections using a new recursion relation.
- Identified branch points at the Euclidean horizon in $1/c$ corrections.

## Abstract

The gauge redundancy of quantum gravity makes the definition of local operators ambiguous, as they depend on the choice of gauge or on a `gravitational dressing' analogous to a choice of Wilson line attachments. Recent work identified exact AdS$_3$ proto-fields by fixing to a Fefferman-Graham gauge. Here we extend that work and define proto-fields with general gravitational dressing. We first study bulk fields charged under a $U(1)$ Chern-Simons gauge theory as an illustrative warm-up, and then generalize the results to gravity. As an application, we compute a gravitational loop correction to the bulk-boundary correlator in the background of a black hole microstate, and then verify this calculation using a newly adapted recursion relation. Branch points at the Euclidean horizon are present in the $1/c$ corrections to semiclassical correlators.