Holography of massive M2-brane theory with discrete torsion

Abstract

AbstractWe investigate the gauge/gravity duality between the $$\mathcal{N} = 6$$N=6 mass-deformed ABJ theory with $$\hbox {U}_k(N+l)\times \hbox {U}_{-k}(N)$$Uk(N+l)×U-k(N) gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(2,1) $$\times $$× SO(4)/$${\mathbb Z}_k\times $$Zk× SO(4)/$${{\mathbb {Z}}}_k$$Zk isometry and the discrete torsion l. For chiral primary operators with conformal dimensions $$\Delta =1,2$$Δ=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 $$\frac{l}{\sqrt{N}}$$lN 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 $${{\mathbb {Z}}}_k$$Zk and the asymptotic discrete torsion l, on the gauge/gravity duality dictionary and on the nature of the asymptotic limits of the LLM geometries.