Spin Structures and AdS$_4$ Holography

TL;DR

This paper explores how different spin structures in 11d supergravity backgrounds of the form AdS4×S7/Zk influence the dual 3d SCFTs, revealing that multiple spin structures can lead to distinct holographic dual theories with varying supersymmetry.

Contribution

It demonstrates that different spin structures on orbifolded supergravity backgrounds can produce dual 3d SCFTs with different supersymmetry levels, illustrated through the AdS4×S7/Z4 case.

Findings

Different spin structures lead to distinct dual SCFTs.

One spin structure corresponds to the ABJM theory at level 4.

Alternative spin structure suggests a different 3d SCFT with less supersymmetry.

Abstract

We study the importance of spin structures as defining data for 11d supergravity backgrounds of the form AdS$_4\times S^7/\mathbf{Z}_k$ with a free orbifold action. For a generic choice of the orbifold action, there is only one spin structure that preserves invariant Killing spinors. There are, however, orbifold actions that allow for more than one spin structure with preserved Killing spinors. In these cases the two different spin structures should lead to distinct holographically dual 3d SCFTs with different amounts of supersymmetry. We illustrate this phenomenon by studying the KK spectrum of 11d supergravity on AdS$_4\times S^7/\mathbf{Z}_4$. For one choice of spin structure this background is dual to the 3d $\mathcal{N}=6$ ABJM theory at level $k=4$. For the alternative choice of spin structure our results suggest that the holographic dual is a different 3d $\mathcal{N}=2$ SCFT and we discuss some of its properties.