Holography for $\mathcal{N}=4$ on $\mathbb{RP}^4$

TL;DR

This paper develops a holographic dual for $ 4$ super Yang-Mills theory on $ p4$, constructing a new supergravity background with a bulk singularity resembling an orientifold plane, advancing the understanding of gauge/gravity duality on nontrivial manifolds.

Contribution

It introduces a novel holographic dual for $ 4$ SYM on $ p4$ by constructing a new BPS supergravity solution with a singularity, extending holography to non-orientable spaces.

Findings

Constructed a dual background in 5D $ 8$ gauged supergravity.

Uplifted the background to a type IIB supergravity solution.

Identified a bulk singularity similar to an orientifold plane.

Abstract

We propose a holographic description of $\mathcal{N}=4$ super Yang-Mills on the four-dimensional real projective space $\mathbb{RP}^4$. We first construct the dual background in the framework of five-dimensional $\mathcal{N}=8$ gauged supergravity, and then uplift it to a new one-half BPS solution of type IIB supergravity. A salient feature of our solution is the presence of a bulk naked singularity whose local behavior resembles that of an O1$_{-}$ plane in flat space.