Non-Orientable AdS$_3$ and its Holography

TL;DR

This paper introduces a novel non-orientable AdS$_3$ spacetime derived as an orientifold of a spinor double cover, revealing a simpler spectrum and a unique CS/WZW correspondence, advancing understanding of non-orientable holography.

Contribution

It constructs a new non-orientable AdS$_3$ solution and demonstrates its simplified spectrum and a distinct CS/WZW correspondence, expanding the scope of holographic dualities.

Findings

New non-orientable AdS$_3$ spacetime derived as an orientifold.

Simpler excited state spectrum in the gravity theory.

Unique CS/WZW correspondence with only one CS term.

Abstract

Known solutions to three-dimensional gravity with negative cosmological constant so far consist of either AdS$_3$ or its orbifolds (or orientifolds). We geometrically derive a novel non-orientable AdS$_3$ spacetime that is an orientifold of a spinor double cover of AdS$_3$, unlike existing solutions. This spacetime's universal cover contains a lightlike instead of spacelike compact direction. We show that its gravity theory possesses a simpler excited state spectrum and exhibits a Chern-Simons/Wess-Zumino-Witt (CS/WZW) correspondence between only one independent CS term and boundary chiral WZW term. This leads us to suggest that CS theory is able to more fully describe non-orientable pure gravity theory compared to orientable gravity.