AdS$_3$ Vacuum State from Four Minkowski Vacuum States

TL;DR

This paper demonstrates that combining four specific Minkowski vacuum states can form a consistent vacuum for a broad class of AdS$_3$ spacetimes with broken parity and time-reversal symmetry, revealing new insights into vacuum structures.

Contribution

It introduces a novel construction of AdS$_3$ vacua from Minkowski states by breaking certain symmetries, expanding understanding of vacuum configurations in lower-dimensional gravity.

Findings

A tensor product of four Minkowski vacua forms a self-consistent AdS$_3$ vacuum.

The construction applies to all AdS$_3$ with non-zero scalar curvature.

Breaking parity and time-reversal symmetry is essential for this vacuum structure.

Abstract

We show that a tensor product of four specific $1{+}2$ Minkowski vacuum states is a self-consistent vacuum state for an infinite set of three-dimensional anti-de Sitter (AdS$_3$) spacetimes if their parity and time-reversal symmetry are broken in a particular way. The infinite set consists of pairs of all AdS$_3$ with non-zero unique scalar curvatures.