Abstract
In this note, we define a holographic dual to four-dimensional superconformal field theories formulated on arbitrary Riemannian manifolds equipped with a Killing vector. Moreover, assuming smoothness of the bulk solution, we study the variation of the holographically renormalized supergravity action in the class of metrics on the boundary four-manifold with a prescribed isometry.
Highlights
JHEP10(2019)115 rotations in the two transverse planes [7], and presented in generality by Nekrasov and Okounkov on an arbitrary manifold [8].1 Its applications have been numerous and influential, including a crucial role in the formulation of the AGT correspondence [9]
As for the topological twist, this construction can be formulated in terms of coupling to a background N = 2 off-shell supergravity [5], and one can formulate the dual supergravity background, as was outlined in the conclusions of [6]
We showed that under certain assumptions of smoothness and existence of the bulk solution, the holographic Ward identity corresponding to the supersymmetric topological twist held
Summary
The results obtained here apply to Ω twists of N = 4 SYM and to (some) conformal field theories of class S [20] (the choice of theory being dependent on the uplift).2 In this context, a computation involving a supersymmetric black hole solution to Romans’ N = 4+ theory has already been precisely matched to a supersymmetric Renyi entropy computed in N = 4 SYM [24]. Since we have gauged the subgroup SU(2)R × U(1)R, we naturally split the generators of the Clifford algebra Cliff(5, 0) corresponding to Spin(5) into ΓI ,. Denoting by ± the projection onto the ±i eigenspaces of Γ45, respectively In this way, there is a natural splitting of the equations between the two eigenspaces
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