Probing Non-Toric Geometry with Rotating Membranes

TL;DR

This paper investigates classical rotating membrane solutions in a non-toric Sasaki-Einstein manifold V_{5,2} within M-theory, exploring their dual operators in a specific 3D N=2 Chern-Simons-matter theory to probe non-toric AdS_4/CFT_3 duality.

Contribution

It provides explicit classical membrane solutions in V_{5,2} and analyzes their dual operators, advancing understanding of non-toric AdS_4/CFT_3 dualities.

Findings

Constructed folded, wrapped, spike, and giant magnon membrane solutions.

Derived dispersion relations for these membrane solutions.

Linked membrane solutions to dual operators in the field theory.

Abstract

Recently Martelli and Sparks presented the first non-toric AdS_4/CFT_3 duality relation between M-theory on AdS_4 x V_{5,2}/Z_k and a class of three-dimensional N=2 quiver Chern-Simons-matter theories. V_{5,2} is a seven-dimensional homogeneneous Sasaki-Einstein manifold with isometry group SO(5)xU(1)_R, which is in general broken to SU(2)xU(1)xU(1)_R by the orbifold projection if k>1. The dual field theory is described by the A_1 quiver, U(N)_k x U(N)_{-k} gauge group, four bifundamentals, two adjoint chiral multiplets interacting via a cubic superpotential. We explore this proposal by studying various classical membrane solutions moving in V_{5,2}. Rotating membrane solutions of folded, wrapped, spike, and giant magnon types are presented with their dispersion relations. We also discuss their dual operators in the Chern-Simons-matter theory.