Narrow Results

In this paper, we will analyze the ABJM theory in harmonic superspace. The harmonic superspace variables will be parametrized by the coset SU(2)/U(1) and thus will have manifest supersymmetry. We will study the quantum gauge transformations and the BRST transformations of this theory in gaugeon formalism. We will use this BRST symmetry to project out the physical subspace from the total Hilbert space. We will also show that the evolution of the -matrix is unitary for this ABJM theory in harmonic superspace.

We report on the exact computation of the S³ partition function of U(N)_k × U(N)_-k ABJM theory for k = 1, N = 1, …, 19. The result is a polynomial in π^-1 with rational coefficients. As an application of our results, we numerically determine the coefficient of the membrane 1-instanton correction to the partition function.

Following Auzzi' work (arXiv:0906.2366), where new vortex solution is found in weak coupled ABJM theory, we apply the ϕ-mapping topological current method to this vortex, and find the multivortices solution could be obtained naturally. Also this multivortices solution gives a clue of the possibility for the antivortex existence. Then we continue to investigate the vortices evolution of the solution, and this leads to the multivortices evolution that used to be hard to handle in conventional vortices scattering theory.

In this paper, we show that the supergravity theory which is dual to ABJM field theory can be consistently reduced to scalar-coupled AdS-Einstein gravity and then consider the reflection symmetric domain wall and its small fluctuation. It is also shown that this domain wall solution is none other than dimensional reduction of M2-brane configuration.

In this paper, we will study aspects relating to the gauge symmetry of the ABJM theory, in ${𝒩}=1$ superspace formalism. We will analyze the ABJM theory in a very general gauge by constructing a generalized gauge fixing term and a generalized ghost term for the ABJM theory. In a certain limit, these generalized gauge fixing and ghost terms will reduce to the gauge fixing and ghost terms for the ABJM theory in Maximal Abelian gauge. Furthermore, in a different limit they will reduce to the gauge fixing and ghost terms for the ABJM theory in Landau gauge. Thus, this very general gauge can be used to interpolates between the ABJM theory in Maximal Abelian gauge and the ABJM theory in Landau gauge. The connection between gauges is also established through generalized BRST approach.

The structures and the associated gauge algebra of ABJM theory in ${𝒩}=1$ superspace are reviewed. We derive the Ward identities of the theory in the class of Lorentz-type gauges at quantum level to justify the renormalizability of the model. We compute the Nielsen identities for the two-point functions of the theory with the help of enlarged BRST transformation. The identities are derived in ABJM theory to ensure the gauge independence of the physical poles of the Green’s functions.

Bi-scalar CFT from $\gamma$ deformed ${𝒩}=4$ SYM describes the fishnet theory which is integrable in the planar limit. The holographic dual of the planar model is the fishchain model. The derivation of the weak–strong duality from the first principle was presented in a recent paper (“The Holographic Fishchain” arXiv:1903.10508). In this paper, we extend the investigation to the tri-scalar CFT which arises from the large twist limit of ABJM theory. We show that it becomes tri-scalar fishnet theory in planar limit and the dual theory is the holographic bi-fishchain model.