# Boundaries and supercurrent multiplets in 3D Landau-Ginzburg models

Brunner, Ilka (0000 0004 1936 973X, grid.5252.0, Arnold Sommerfeld Center, Ludwig-Maximilians-Universität, Theresienstraße 37, 80333, München, Germany) ; Schulz, Jonathan (0000 0004 1936 973X, grid.5252.0, Arnold Sommerfeld Center, Ludwig-Maximilians-Universität, Theresienstraße 37, 80333, München, Germany) ; Tabler, Alexander (0000 0004 1936 973X, grid.5252.0, Arnold Sommerfeld Center, Ludwig-Maximilians-Universität, Theresienstraße 37, 80333, München, Germany)

13 June 2019

Abstract: Theories with 3D N = 2 $\mathcal{N} = 2$ bulk supersymmetry may preserve a 2D N = 0 , 2 $\mathcal{N} = \left(0,\ 2\right)$ 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 Q ¯ + ${\overline{Q}}_{+}$ -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.

Published in: JHEP 1906 (2019) 046 DOI: 10.1007/JHEP06(2019)046
arXiv: 1904.07258