Non-orientable AdS3 and its holography

Abstract

Known solutions to three-dimensional gravity with negative cosmological constant consist of either AdS₃ or its orbifolds (or orientifolds). We geometrically derive a novel non-orientable AdS₃ spacetime that is an orientifold of a spinor double cover of AdS₃. This spacetime’s universal cover contains a lightlike compact direction instead of AdS₃’s spacelike compact direction. We show that its gravity theory possesses a simpler excited state spectrum and a Chern-Simons/Wess-Zumino-Witt (CS/WZW) correspondence between a single 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.