Non-Orientable AdS${}_3$ and its Holography

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.