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arXiv · 1409.6713

Localization of 3d $\mathcal{N}=2$ Supersymmetric Theories on $S^1 \times D^2$

Yutaka Yoshida·Katsuyuki Sugiyama
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Abstract

We study three dimensional $\mathcal{N}=2$ supersymmetric Chern-Simons-Matter theories on the direct product of a circle and a two dimensional hemisphere ($S^1 \times D^2$) with specified boundary conditions by the method of localization. We construct boundary interactions to cancel the supersymmetric variation of the three dimensional superpotential term and the Chern-Simons term and show inflows of the bulk-boundary anomalies. It finds that the boundary conditions induce two dimensional $\mathcal{N}=(0,2)$ type supersymmetry on the boundary torus. We also study the relation between the 3d-2d coupled partition function of our model and three dimensional holomorphic blocks.

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Yutaka Yoshida, Katsuyuki Sugiyama. 2014-09-23. Localization of 3d $\mathcal{N}=2$ Supersymmetric Theories on $S^1 \times D^2$. https://doi.org/10.1093/ptep/ptaa136

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