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Register a new userHolography of Massive M2-brane Theory with Discrete Torsion
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We investigate the gauge/gravity duality between the ${cal N} = 6$ mass-deformed ABJ theory with U$_k(N+l)times$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.
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We define and compute algebraically a perturbative part of protected sphere correlation functions in the M2 brane SCFTs. These correlation functions are expected to have a holographic description in terms of twisted, $Omega$-deformed M-theory. We uncover a hidden perturbative triality symmetry which supports this conjecture. We also discuss some variants of the setup, involving M2 branes at $A_k$ singularities and D3 branes with a transverse compact direction.
We present the formulation of the bosonic Hamiltonian M2-brane compactified on a twice punctured torus following the procedure proposed in cite{mpgm14}. In this work we analyse two possible metric choice, different from the one used in cite{mpgm14}, over the target space and study some of the properties of the corresponding Hamiltonian.
We study partition functions of low-energy effective theories of M2-branes, whose type IIB brane constructions include orientifolds. We mainly focus on circular quiver superconformal Chern-Simons theory on $S^3$, whose gauge group is $O(2N+1)times USp(2N)times cdots times O(2N+1)times USp(2N)$. This theory is the natural generalization of the $mathcal{N}=5$ ABJM theory with the gauge group $O(2N+1)_{2k} times USp(2N)_{-k}$. We find that the partition function of this type of theory has a simple relation to the one of the M2-brane theory without the orientifolds, whose gauge group is $U(N)times cdots times U(N)$. By using this relation, we determine an exact form of the grand partition function of the $O(2N+1)_{2} times USp(2N)_{-1}$ ABJM theory, where its supersymmetry is expected to be enhanced to $mathcal{N}=6$. As another interesting application, we discuss that our result gives a natural physical interpretation of a relation between the grand partition functions of the $U(N+1)_4 times U(N)_{-4}$ ABJ theory and $U(N)_2 times U(N)_{-2}$ ABJM theory, recently conjectured by Grassi-Hatsuda-Mari~no. We also argue that partition functions of $hat{A}_3$ quiver theories have representations in terms of an ideal Fermi gas systems associated with $hat{D}$-type quiver theories and this leads an interesting relation between certain $U(N)$ and $USp(2N)$ supersymmetric gauge theories.
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