New $AdS_4\times X_7$ Geometries with $\mathcal{N}=6$ in M Theory

TL;DR

This paper introduces new supersymmetric AdS_4 x X_7 solutions in M theory with specific isometries, deriving geometric properties and discussing dual 3D superconformal field theories with rac{N}{3} supersymmetry.

Contribution

It constructs new rac{N}{6} supersymmetric AdS_4 solutions with tri-Sasakian spaces derived from hyperkahler quotients, expanding known geometries in M theory.

Findings

Computed volumes of X_7 and supersymmetric cycles using localization.

Identified dual 3D superconformal field theories with rac{N}{3} supersymmetry.

Connected geometric properties to field theory duals.

Abstract

We study supersymmetric AdS_4 x X_7 solutions of 11-dim supergravity where the tri-Sasakian space X_7 has generically U(1)^2\times SU(2)_R isometry. The compact and regular 7-dim spaces X_7=S(t_1,t_2,t_3) is originated from 8-dim hyperkahler quotient of a 12-dim flat hyperkahler space by U(1) and belongs to the class of the Eschenburg space. We calculate the volume of X_7 and that of the supersymmetric five cycle via localization. From this we discuss the 3-dim dual superconformal field theories with \CN=3 supersymmetry.