Exactly Marginal Deformations and their Supergravity Duals

TL;DR

This paper explores the supergravity duals of exactly marginal deformations in $ ext{AdS}_5$ solutions, revealing a geometric structure encoding the superpotential and providing solutions for generic $ ext{N}=1$ deformations of $ ext{N}=4$ SYM.

Contribution

It introduces a geometric framework for constructing supergravity duals of $ ext{N}=1$ conformal deformations, solving a longstanding problem in holography.

Findings

Identifies a generalised holomorphic structure in supergravity backgrounds.

Provides a method to construct duals of generic $ ext{N}=1$ deformations.

Derives a new Hilbert series formula for deformed field theories.

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.