Abstract
Theories with 3D mathcal{N} = 2 bulk supersymmetry may preserve a 2D mathcal{N} = left(0, 2right) subalgebra when a boundary is introduced, possibly with localized degrees of freedom. We propose generalized supercurrent multiplets with bulk and boundary parts adapted to such setups. Using their structure, we comment on implications for the {overline{Q}}_{+} -cohomology. As an example, we apply the developed framework to Landau-Ginzburg models. In these models, we study the role of boundary degrees of freedom and matrix factorizations. We verify our results using quantization.
Highlights
In this paper we study N = 2 supersymmetric theories in flat (2+1)-dimensional spacetime with boundaries
We consider the consequences of the supercurrent multiplets for the case that the N = (0, 2) supersymmetry is the symmetry preserved at the boundary of a three-dimensional theory
In this paper we analyzed three-dimensional theories with N = 2 supersymmetry from various points of view: we constructed the symmetry currents by developing an extension of Noether’s procedure, we considered the supermultiplets in the boundary situation and we commented on the Q+-cohomology in a possible half-twisted theory
Summary
In the case of pure bulk theories, it is very useful to arrange the supercurrents together with other conserved currents into multiplets. Conformal symmetry is part of the chiral algebra Given these findings, we consider the consequences of the supercurrent multiplets for the case that the N = (0, 2) supersymmetry is the symmetry preserved at the boundary of a three-dimensional theory. We discuss an integrated structure, where we integrate in the direction perpendicular to the boundary This provides a two-dimensional version of the conservation equations, taking the familiar form of divergence-freeness of the currents. By imposing canonical commutation relations for the bulk and boundary fields, we verify that the supercharges implement the correct symmetry transformations on the fields and their derivatives, and we compute the brackets between supercharges and supercurrents.
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