Marginal Deformations of Field Theories with AdS_4 Duals

TL;DR

The paper extends the Lunin–Maldacena gamma-deformation to eleven-dimensional AdS$_4$ backgrounds by exploiting $X_7$ with $U(1)^3$ isometry, yielding new $AdS_4$ solutions that preserve varying amounts of supersymmetry. It provides explicit transformation rules for the metric and four-form flux, and identifies the dual exactly marginal operators in the corresponding $d=3$ SCFTs for several key examples ($M(3,2)$, $Q(1,1,1)$, $N(1,1)_I$), including a match between baryonic 5-cycle volumes and operator dimensions. The work connects geometric deformations to field-theory superpotentials, illustrating how marginal deformations can be constructed and understood in AdS$_4$/CFT$_3$ contexts. It also discusses potential non-supersymmetric generalizations and future directions for identifying additional marginal deformations in these 3d theories.

Abstract

We generate new AdS_4 solutions of D=11 supergravity starting from AdS_4 x X_7 solutions where X_7 has U(1)^3 isometry. We consider examples where X_7 is weak G_2, Sasaki-Einstein or tri-Sasakian, corresponding to d=3 SCFTs with N=1,2 or 3 supersymmetry, respectively, and where the deformed solutions preserve N=1,2 or 1 supersymmetry, respectively. For the special cases when X_7 is M(3,2), Q(1,1,1) or N(1,1)_I we identify the exactly marginal deformation in the dual field theory. We also show that the volume of supersymmetric 5-cycles of N(1,1)_I agrees with the conformal dimension predicted by the baryons of the dual field theory.

Figures (2)

• Figure 1: The quiver diagrams for the $Q(1,1,1)$ and $M(3,2)$ field theories.
• Figure 2: The quiver diagram for the $N(1,1)_I$ field theory.