Exactly Marginal Deformations and their Supergravity Duals

Abstract

We study the space of supersymmetric AdS${}_5$ solutions of type IIB supergravity corresponding to the conformal manifold of the dual $\mathcal{N}=1$ conformal field theory. We show that the background geometry naturally encodes a generalised holomorphic structure, dual to the superpotential of the field theory, with the existence of the full solution following from a continuity argument. In particular, this provides a solution to the long-standing problem of finding the gravity dual of the generic $\mathcal{N}=1$ deformations of $\mathcal{N}=4$ conformal field theory. Using this formalism, we derive a new result for the Hilbert series of the deformed field theories.

5 pages

References in corpus (3)

• Generalised Geometry for M-Theory
• Reformulating Supersymmetry with a Generalized Dolbeault Operator
• From $\beta$ to $\eta$: a new cohomology for deformed Sasaki-Einstein manifolds