Holography of massive M2-brane theory with discrete torsion

Abstract

Abstract We 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.