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Register a new userThe M2-brane over the twisted torus with punctures
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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.
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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 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.
The formulation of supermembrane theory on nontrivial backgrounds is discussed. In particular, we obtain the Hamiltonian of the supermembrane on a background with constant bosonic three form on a target space $M_9 times T^2$.
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.
We show how the SL(5) duality in M-theory is explained from a canonical analysis of M2-brane mechanics. Diffeomorphism constraints for a M2-brane coupled to supergravity background in d=4 are reformulated in a SL(5) covariant form, in which spatial diffeomorphism constraints are recast into a SL(5) vector and the generalized metric in the Hamiltonian constraint is quartic in the SL(5) generalized vielbein. The Hamiltonian for a M2 brane has the SL(5) duality symmetry in a background dependent gauge.
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