Holography of massive M2-brane theory with discrete torsion

Abstract

We investigate the gauge/gravity duality between the mathcal{N} = 6 mass-deformed ABJ theory with hbox {U}_k(N+l)times hbox {U}_{-k}(N) gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(2,1) times SO(4)/{mathbb Z}_ktimes SO(4)/{{mathbb {Z}}}_k isometry and the discrete torsion l. For chiral primary operators with conformal dimensions Delta =1,2, we obtain the exact vacuum expectation values using the holographic method in 11-dimensional supergravity and show that the results depend on the shapes of droplet pictures in LLM geometries. The frac{l}{sqrt{N}} contributions from the discrete torsion l for several simple droplet pictures in the large N limit are determined in holographic vacuum expectation values. We also explore the effects of the orbifolding {{mathbb {Z}}}_k and the asymptotic discrete torsion l, on the gauge/gravity duality dictionary and on the nature of the asymptotic limits of the LLM geometries.