Holography of massive ABJM theory with discrete torsion

Abstract

We investigate the gauge/gravity duality between the Ν=6 mass-deformed ABJ theory with Uk(N+l)×U−k(N) gauge symmetry and 11-dimensional supergravity on LLM geometries with SO(2,1)×SO(4)/ℤk×SO(4)/ℤk isometry and the discrete torsion l. We obtain the vacuum expectation values (vevs) of chiral primary operators (CPOs) with conformal dimension one for the supersymmetric vacuum solusions in the mass-deformed ABJ (mABJ) theory, and compare it to dual quantities obtained by using the holographic method in 11-dimensional supergravity. In the large N limit, we show that the vevs are in exact agreement with the holographic quantities for all supersymmetric vacuum solutions. For LLM geometries with the discrete torsion, the holo-graphic results comprise 1/N corrections. We also explore the effects of the orbifolding on the gauge/gravity duality dictionary and on the nature of the asymptotic limits of the LLM geometries.