Spin structures and AdS4 holography

Abstract

We study the importance of spin structures as defining data for 11d supergravity backgrounds of the form AdS4 × S7/Zk 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 AdS4 × S7/Z4. For one choice of spin structure this background is dual to the 3d $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = 2 SCFT and we discuss some of its properties.

Large N partition functions of the ABJM theory

“…we have N = N for k = 4 as can be seen from (4.61). We do not yet understand the significance (if any) of this observation and any possible relation to the recent analysis of the holography for the k = 4 ABJM theory in [69].…”