Wrapped M5-branes and complex saddle points

Abstract

We study the effects of the introduction of a ϑ term in minimal gauged supergravity in four dimensions. We show why this term is not present in supergravity duals of field theories arising on wrapped M2-branes, but is there in the case of M5-branes wrapping hyperbolic manifolds Σ3, and compute the higher-derivative corrections. Having proved that the on-shell supergravity action of any supersymmetric solution can be expressed in terms of data from the fixed points of a Killing vector, we show that it is proportional to a complex topological invariant of Σ3. This is consistent with the characteristics of the dual three-dimensional 𝒩= 2 SCFT predicted by the 3d-3d correspondence, and we match the large N limit of its partition functions in the known cases.

Comments on holographic level/rank dualities

“…Another avenue is to investigate non-trivial topologies of the 3d spacetime for which the framing anomaly is relevant, and see how it matches with analogous couplings on the brane actions (similarly as in [32]) and in the bulk. Finally, it would be interesting to find a more satisfying understanding of the holographic dual of the T operation, namely a 10d interpretation of the operation of turning on an integer θ term for C, as discussed below (3.59) (see [33] for a discussion of a similar problem in 11d supergravity).…”

Comments on Holographic Level/Rank Dualities

“…Another avenue is to investigate non-trivial topologies of the 3d spacetime for which the framing anomaly is relevant, and see how it matches with analogous couplings on the brane actions (similarly as in [32]) and in the bulk. Finally, it would be interesting to find a more satisfying understanding of the holographic dual of the T operation, namely a 10d interpretation of the operation of turning on an integer θ term for C, as discussed below (3.62) (see [33] for a discussion of a similar problem in 11d supergravity).…”