Marginal Deformations with U(1)^3 Global Symmetry

TL;DR

This work extends the Lunin–Maldacena marginal deformation program to eleven-dimensional backgrounds of the form ${\rm AdS}_4\times Y_7$ where $Y_7$ is a Sasaki–Einstein space with $U(1)^3$ isometry. By performing an $SL(2,\mathbb{R})$ transformation on a ${\bf T}^2$ within a type IIB reduction, followed by T-duality and uplifting, the authors generate new regular warped ${\rm AdS}_4$ solutions with deformed $F_{(4)}$ and warp factor $G$, corresponding to marginal deformations of the dual three-dimensional gauge theories. They construct explicit deformations for ${\rm AdS}_4\times Q^{1,1,1}$ and for infinite families $Z^{p,q,r,s}$, as well as their cohomogeneity-three cousins $L^{p,q,r,s}$ and the ${\rm AdS}_4\times M^{1,1,1}$ case, with the deformed backgrounds preserving ${\cal N}=2$ supersymmetry and remaining completely regular. The results illuminate the structure of marginal deformations in 3D SCFTs and point to broader applications, including warped KK embeddings and analyses of spectra and RG flows in the dual theories.

Abstract

We generate new 11-dimensional supergravity solutions from deformations based on U(1)^3 symmetries. The initial geometries are of the form AdS_4 x Y_7, where Y_7 is a 7-dimensional Sasaki-Einstein space. We consider a general family of cohomogeneity one Sasaki-Einstein spaces, as well as the recently-constructed cohomogeneity three L^{p,q,r,s} spaces. For certain cases, such as when the Sasaki-Einstein space is S^7, Q^{1,1,1} or M^{1,1,1}, the deformed gravity solutions correspond to a marginal deformation of a known dual gauge theory.

Figures (2)

• Figure 1: Flow diagram for 5-dimensional Sasaki-Einstein spaces
• Figure 2: Flow diagram for 7-dimensional Sasaki-Einstein spaces