N=8 SCFT and M Theory on AdS_4 x RP^7

TL;DR

The paper addresses how to realize and interpret the holographic dual of a 3d $N=8$ SCFT by studying M-theory on $AdS_4 \times RP^7$. It extends Witten's orientifold construction to RP^7, classifies possible brane wrappings using the (co)homology of RP^7 and the discrete torsion in $H^3(RP^7,Z)$ and $H^4(RP^7,Z)$, and derives the field-theory implications for domain walls and baryon vertices in SU(N) and SO/Sp(2N) gauge theories. The SU(N) baryon vertex arises from a wrapped M5 on a 5-cycle of $S^7$, giving a scaling dimension $\Delta = N/2$, while the baryon vertex in SO(N)/Sp(2N) is realized by an M5 wrapped on RP^5 with stability controlled by $H_5(RP^7,Z) \cong Z_2$ and possible decay channels governed by discrete torsion. The work thus provides a top-down holographic framework for nonperturbative objects in 3d $N=8$ SCFTs and identifies open questions related to instanton corrections, discrete torsion, and extensions to other seven-dimensional internal manifolds.

Abstract

We study M theory on $AdS_4 \times \RP^7$ corresponding to 3 dimensional ${\cal N}=8$ superconformal field theory which is the strong coupling limit of 3 dimensional super Yang-Mills theory. For SU(N) theory, a wrapped M5 brane on $\RP^5$ can be interpreted as baryon vertex. For $SO(N)/Sp(2N)$ theory, by using the property of (co-)homology of $\RP^7$, we classify various wrapping branes and consider domain walls and the baryon vertex.