A Killing Vector Treatment of Multiboundary Wormholes

TL;DR

This paper derives explicit Killing vectors for three-boundary wormholes in AdS3, expanding the toolkit for exploring multiboundary geometries and their role in quantum gravity.

Contribution

It provides a systematic method to construct three-boundary wormholes with full moduli space coverage, including rotating and non-rotating cases, and generalizes to higher genus spaces.

Findings

Explicit Killing vectors for three-boundary wormholes derived

Method captures the full moduli space of such wormholes

Generalization to higher genus multiboundary spaces achieved

Abstract

The two-sided BTZ black hole has been instrumental in elucidating several aspects of AdS/CFT. Similarly, multiboundary wormholes provide a useful and rich arena in which probing questions of quantum gravity can be posed and explored. In this work, we find the explicit forms of the Killing vectors needed to construct three-boundary wormholes, with and without rotation, as quotients of AdS$_3$. We ensure that our method captures the full moduli space of such wormholes and elaborate on the generalization of our procedure to more exotic multiboundary spaces, including higher genus.