We consider the quantum spectral problem appearing the Fermi gas formulation of the ABJM (Aharony-Bergman-Jafferis-Maldacena) matrix model. This is known to related to the refined topological string on local P1×P1 Calabi-Yau geometry. In the ABJM setting the problem is formulated by an integral equation, and is somewhat different from the one formulated directly in terms of the Calabi-Yau geome...

We study marginal deformations of superconformal Chern-Simons matter theories that are based on 3-algebras. For this, we introduce the notion of an associated 3-product, which captures very general gauge invariant deformations of the superpotentials of the BLG and ABJM models. We also consider conformal multi-trace deformations preserving N = 2 supersymmetry. We then use N = 2 supergraph techni...

We consider twist-Ä operators in the planar AE superconformal Chern-Simons ABJM theory. Their anomalous dimension ­ Ë Ä ´AEµ is a function of the twist Ä, the spin AE, and the dressed coupling of ABJM. We show that at next-to-leading order in the large spin expansion, this anomalous dimension is related to that of AE SYM twist operators by a simple scaling law.

We study Aharony-Bergman-Jafferis-Maldacena (ABJM) theory without and with mass deformation. It is shown that maximally supersymmetry preserving, D-term, and F-term mass deformations of single mass parameter are equivalent. We obtain vortex-type halfBPS equations and the corresponding energy bound. For the undeformed ABJM theory, the resulting half-BPS equation is the same as that in supersymme...

In arXiv:0806.0363 the worldvolume superalgebra of the N = 8 Bagger-Lambert theory was calculated. In this paper we derive the general form for the worldvolume superalgebra of the N = 6 Bagger-Lambert theory. For a particular choice of three-algebra we derive the superalgebra of the ABJM theory. We interpret the associated central charges in terms of BPS brane configurations. In particular we f...

We tabulate various properties of the ‘language’ of N = 6 Chern-Simons Theory, in the sense of Polyakov. Specifically we enumerate and compute character formulas for all syllables of up to four letters, i.e. all irreducible representations of OSp(6|4) built from up to four fundamental fields of the ABJM theory. We also present all tensor product decompositions for up to four singletons and list...

We consider the link average of the half-BPS Wilson loop operators in N = 6 superconformal Chern-Simons-matter theory, which is called ABJM theory. We show that this loop average is reduced to a (super)matrix integral by the localization method, in a similar way to the bosonic U(N) Chern-Simons theory. Using this matrix integral, we compute the twoand three-link averages with an operator formal...

We study the integrability properties of Wilson loops in ${\cal N}=6$ three-dimensional Chern-Simons-matter (ABJM) theory. begin with construction an open spin chain that describes anomalous dimensions operators inserted along contour a 1/2 BPS loop. Moreover, we compute all-loop reflection matrices govern interaction spin-chain excitations boundary, including their dressing factors, and check ...

We study remarkable connections between twistor-string formulas for tree amplitudes in ${\cal N}=4$ SYM and N}=6$ ABJM, the corresponding momentum amplituhedron kinematic space of $D=4$ $D=3$, respectively. Based on Veronese map to positive Grassmannians, we define a from $G_{+}(2,n)$ $(2n{-}4)$-dimensional subspace 4d where lives. provide strong evidence that is diffeomorphism $G_+(2,n)$ inter...