Many three-dimensional N = 2 SCFTs admit a universal partial topological twist when placed on hyperbolic Riemann surfaces. We exploit this fact to derive a universal formula which relates the planar limit of the topologically twisted index of these SCFTs and their three-sphere partition function. We then utilize this to account for the entropy of a large class of supersymmetric asymptotically AdS 4 magnetically charged black holes in Mtheory and massive type IIA string theory. In this context we also discuss novel AdS 2 solutions of eleven-dimensional supergravity which describe the near horizon region of large new families of supersymmetric black holes arising from M2-branes wrapping Riemann surfaces.

We find a large class of two-dimensional N = (0, 2) SCFTs obtained by compactifying four-dimensional N = 1 quiver gauge theories on a Riemann surface. We study these theories using anomalies and c-extremization. The gravitational duals to these fixed points are new AdS 3 solutions of IIB supergravity which we exhibit explicitly. Along the way we uncover a universal relation between the conformal anomaly coefficients of fourdimensional and two-dimensional SCFTs connected by an RG flow across dimensions. We also observe an interesting novel phenomenon in which the superconformal R-symmetry mixes with baryonic symmetries along the RG flow.

We study RG flows between superconformal field theories living in different spacetime dimensions which exhibit universal properties, independent of the details of the UV and IR theories. In particular, when the UV and IR theories are both even-dimensional we establish exact universal relations between their conformal anomaly coefficients. We also provide strong evidence for similar relations between appropriately defined free energies for RG flows between odd-dimensional theories in the large N limit. Holographically, these RG flows across dimensions are described by asymptotically AdS black branes in a gauged supergravity theory, which we exhibit explicitly. We also discuss the uplift of these solutions to string and M-theory and comment on how the entropy of such black branes is captured by the dual field theory.

We derive the partition function of 5d N = 1 gauge theories on the manifold S 3 b × Σ g with a partial topological twist along the Riemann surface, Σ g . This setup is a higher dimensional uplift of the two-dimensional A-twist, and the result can be expressed as a sum over solutions of Bethe-Ansatz-type equations, with the computation receiving nontrivial non-perturbative contributions. We study this partition function in the large N limit, where it is related to holographic RG flows between asymptotically locally AdS 6 and AdS 4 spacetimes, reproducing known holographic relations between the corresponding free energies on S 5 and S 3 and predicting new ones. We also consider cases where the 5d theory admits a UV completion as a 6d SCFT, such as the maximally supersymmetric N = 2 Yang-Mills theory, in which case the partition function computes the 4d index of general class S theories, which we verify in certain simplifying limits. Finally, we comment on the generalization to M 3 × Σ g with more general three-manifolds M 3 and focus in particular on M 3 = Σ g × S 1 , in which case the partition function relates to the entropy of black holes in AdS 6 . β 67 A.1 5d maximal theory and class S 68 A.2 Class S k theories 70 A.3 E-string theory 72 B Instanton partition function for N = 2 U(N ) and SU(N ) SYM 74This preserves an SU(2) × U(1) isometry, and the Killing vector appearing in the superalgebra is K = ∂ ψ . Then, in this background we have 44], and so the central charge in the N = (2, 2) algebra (2.15) iswhich defines a variable, σ, valued in the complexification of the Cartan subalgebra of the flavor symmetry, which is a holomorphic combination of the background real scalar, z, and component, A ψ , of the background gauge field along the direction K, as discussed in more detail in [11]. The 2d A-twist and Bethe Ansatz equationsAs observed above, the supersymmetric background on S 3 b × Σ g , when considered along the Σ g directions, takes the form of a 2d topological twist. Such setups, where a d-dimensional 5 We will return to consider more general lens spaces in section 5.

We study a supersymmetric, rotating, electrically charged black hole in AdS 4 which is a solution of four-dimensional minimal gauged supergravity. Using holography we show that the free energy on S 3 and the superconformal index of the dual three-dimensional N = 2 SCFT, in the planar limit, are related in a simple universal way. This result applies to large classes of SCFTs constructed from branes in string and M-theory which we discuss in some detail. For theories of class R, which arise from N M5-branes wrapped on hyperbolic three-manifolds, we show that the superconformal index agrees with the black hole entropy in the large N limit. arXiv:1909.05873v2 [hep-th]

We apply the matrix model of Kapustin, Willett and Yaakov to compute the free energy of N = 3 Chern-Simons matter theories with D n quivers in the large N limit. We conjecture a general expression for the free energy that is explicitly invariant under Seiberg duality and show that it can be interpreted as a sum over certain graphs known as signed graphs. Through the AdS/CFT correspondence, this leads to a prediction for the volume of certain tri-Sasaki Einstein manifolds. We also study the unfolding procedure, which relates these D n quivers to A 2n−5 quivers. Furthermore, we consider the addition of massive fundamental flavor fields, verifying that integrating these out decreases the free energy in accordance with the F-theorem.

We consider a family of deformations of T 1,1 in the Yang-Baxter sigma model approach. We first discuss a supercoset description of T 1,1 , which makes manifest the full symmetry of the space and leads to the standard Sasaki-Einstein metric. Next, we consider three-parameter deformations of T 1,1 by using classical r-matrices satisfying the classical Yang-Baxter equation (CYBE). The resulting metric and NS-NS two-form agree exactly with the ones obtained via TsT transformations, and contain the Lunin-Maldacena background as a special case. It is worth noting that for AdS 5 × T 1,1 , classical integrability for the full sector has been argued to be lost. Hence our result indicates that the YangBaxter sigma model approach is applicable even for non-integrable cosets. This observation suggests that the gravity/CYBE correspondence can be extended beyond integrable cases.

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