Exactly Marginal Deformations and Their Supergravity Duals

Anthony Ashmore (1) , Michela Petrini (1) , Edward Tasker , Daniel Waldram

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

We study the space of supersymmetric ${\mathrm{AdS}}_5$ 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 generalized 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 work allows us to address the long-standing problem of finding the gravity dual of the generic $\mathcal{N}=1$ deformations of $\mathcal{N}=4$ conformal field theory: even if we are not able to give it in a fully explicit form, we provide a proof-of-existence of the supergravity solution. Using this formalism, we derive a new result for the Hilbert series of the deformed field theories.

Mots clés: field theory: conformal; deformation: marginal; background: geometry; gravitation: duality; supergravity: Type IIB; holomorphic; superpotential; supersymmetry: 1; AdS(5)

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Anthony Ashmore, Michela Petrini, Edward Tasker, Daniel Waldram. Exactly Marginal Deformations and Their Supergravity Duals. Physical Review Letters, 2022, 128 (19), pp.191601. ⟨10.1103/PhysRevLett.128.191601⟩. ⟨hal-03512654⟩