# Chiral boundary conditions for singletons and W-branes

## TL;DR

This paper explores chiral boundary conditions in AdS3 holography, showing they accommodate singleton solutions and are relevant for black hole microstate geometries, challenging full conformal invariance preservation.

## Contribution

It introduces a generalized chiral boundary condition framework that includes singleton solutions and connects to black hole microstate proposals.

## Key findings

- Singleton solutions fit within chiral boundary conditions.
- Full conformal invariance cannot be preserved with singleton boundary conditions.
- Chiral boundary conditions include extremal BTZ black holes.

## Abstract

We revisit the holographic dictionary for a free massless scalar in AdS$_3$, focusing on the `singleton' solutions for which the boundary profile is an arbitrary chiral function. We look for consistent boundary conditions which include this class of solutions. On one hand, we give a no-go argument that they cannot be interpreted within any boundary condition which preserves full conformal invariance. On the other hand, we show that such solutions fit naturally in a generalization of the Comp\`{e}re-Song-Strominger boundary conditions, which preserve a chiral Virasoro and current algebra. These observations have implications for the black hole deconstruction proposal, which proposes singleton solutions as candidate black hole microstate geometries. Our results suggest that the chiral boundary condition, which also contains the extremal BTZ black hole, is the natural setting for holographically interpreting the black hole deconstruction proposal.