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Register a new userNew conformal field theory from $mathcal{N}=(0,2)$ Landau-Ginzburg model
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By studying the infra-red fixed point of an $mathcal{N}=(0,2)$ Landau-Ginzburg model, we find an example of modular invariant partition function beyond the ADE classification. This stems from the fact that a part of the left-moving sector is a new conformal field theory which is a variant of the parafermion model.
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In this paper we study the low energy physics of Landau-Ginzburg models with N=(0,2) supersymmetry. We exhibit a number of classes of relatively simple LG models where the conformal field theory at the low energy fixed point can be explicitly identified. One interesting class of fixed points can be thought of as heterotic minimal models. Other examples include N=(0,2) renormalization group flows that end up at N=(2,2) minimal models and models with non-abelian symmetry.
It is believed that the two-dimensional massless $mathcal{N}=2$ Wess--Zumino model becomes the $mathcal{N}=2$ superconformal field theory (SCFT) in the infrared (IR) limit. We examine this theoretical conjecture of the Landau--Ginzburg (LG) description of the $mathcal{N}=2$ SCFT by numerical simulations on the basis of a supersymmetric-invariant momentum-cutoff regularization. We study a single supermultiplet with cubic and quartic superpotentials. From two-point correlation functions in the IR region, we measure the scaling dimension and the central charge, which are consistent with the conjectured LG description of the $A_2$ and $A_3$ minimal models, respectively. Our result supports the theoretical conjecture and, at the same time, indicates a possible computational method of correlation functions in the $mathcal{N}=2$ SCFT from the LG description.
We consider the general $mathcal{N}{=},4,$ $d{=},3$ Galilean superalgebra with arbitrary central charges and study its dynamical realizations. Using the nonlinear realization techniques, we introduce a class of actions for $mathcal{N}{=},4$ three-dimensional non-relativistic superparticle, such that they are linear in the central charge Maurer-Cartan one-forms. As a prerequisite to the quantization, we analyze the phase space constraints structure of our model for various choices of the central charges. The first class constraints generate gauge transformations, involving fermionic $kappa$-gauge transformations. The quantization of the model gives rise to the collection of free $mathcal{N}{=},4$, $d{=},3$ Galilean superfields, which can be further employed, e.g., for description of three-dimensional non-relativistic $mathcal{N}{=},4$ supersymmetric theories.
The maximal extension of supersymmetric Chern-Simons theory coupled to fundamental matter has $mathcal{N} = 3$ supersymmetry. In this short note, we provide the explicit form of the action for the mass-deformed $mathcal{N} = 3$ supersymmetric $U(N)$ Chern-Simons-Matter theory. The theory admits a unique triplet mass deformation term consistent with supersymmetry. We explicitly construct the mass-deformed $mathcal{N} = 3$ theory in $mathcal{N} = 1$ superspace using a fundamental and an anti-fundamental superfield.
We study $mathcal{N} = 3$ supersymmetric Chern-Simons-matter theory coupled to matter in the fundamental representation of $SU(N)$. In the t Hooft large $N$ limit, we compute the exact $2 to 2$ scattering amplitudes of the fundamental scalar superfields to all orders in the t Hooft coupling $lambda$. Our computations are presented in $mathcal{N} = 1$ superspace and make significant use of the residual $SO(2)_R$ symmetry in order to solve for the exact four-point correlator of the scalar superfields. By taking the on-shell limit, we are able to extract the exact $2 to 2$ scattering amplitudes of bosons/fermions in the symmetric, anti-symmetric and adjoint channels of scattering. We find that the scattering amplitude of the $mathcal{N} = 3$ theory in the planar limit is tree-level exact to all orders in the t Hooft coupling $lambda$. The result is consistent with the conjectured bosonization duality and is expected to have enhanced symmetry structures such as dual superconformal symmetry and Yangian symmetry.
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