Wrapped $M5$-branes and complex saddle points

Abstract

We study the effects of the introduction of a $\vartheta$ 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 ${\Sigma }_3$, 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 ${\Sigma }_3$. This is consistent with the characteristics of the dual three-dimensional $\mathcal{N}=2$ SCFT predicted by the $3d$-$3d$ correspondence, and we match the large $N$ limit of its partition functions in the known cases.

44 pages; v2: references added, revised argument in section 4

References in corpus (12)

• Boundary Conditions and Dualities: Vector Fields in AdS/CFT
• Consistent Kaluza-Klein Reductions for General Supersymmetric AdS Solutions
• Wrapped M5-branes, consistent truncations and AdS/CMT
• Thermodynamics of accelerating and supersymmetric $Ad{S}_4$ black holes
• AdS spacetimes from wrapped M5 branes
• A gravity interpretation for the Bethe Ansatz expansion of the $\mathcal{N}=4$ SYM index
• Holographic renormalization and supersymmetry
• Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence
• Cosmological Einstein-Maxwell Instantons and Euclidean Supersymmetry: Beyond Self-Duality
• Holography of 3d-3d correspondence at Large N
• Factorization of log-corrections in AdS${}_4$/CFT${}_3$ from supergravity localization
• The Supersymmetry of Higher-Derivative Supergravity in AdS${}_4$ Holography