AdS/CFT with Tri-Sasakian Manifolds

TL;DR

This paper explores the AdS/CFT correspondence involving Tri-Sasakian 7-manifolds in M-theory, calculating geometric volumes and proposing dual gauge theories for N=3 superconformal field theories in three dimensions.

Contribution

It introduces a method to compute volumes and conformal dimensions for Tri-Sasakian manifolds and proposes quiver gauge theories as their duals in the AdS/CFT framework.

Findings

Volumes of Tri-Sasakian manifolds calculated

Conformal dimensions of baryonic operators derived

Proposed quiver gauge theories as dual descriptions

Abstract

We consider generic toric Tri-Sasakian 7-manifolds X_7 in the context of M-theory on AdS_4 X X_7 and study their AdS/CFT correspondence to N=3 SCFT in 3D spacetime. We obtain volumes of Tri-Sasakian manifolds and their supersymmetric 5-cycles via cohomological integration technique, and use this to calculate conformal dimensions of baryonic operators in the SCFT side. We also propose quiver-type gauge theories for UV description of the corresponding N=3 SCFT.