2020年7月15日

# Supersymmetric indices on $I \times T^2$, elliptic genera and dualities with boundaries

• Katsuyuki Sugiyama
• ,
• Yutaka Yoshida

DOI
10.1016/j.nuclphysb.2020.115168

We study three dimensional $\mathcal{N}=2$ supersymmetric theories on $I \times M_2$ with 2d $\mathcal{N}=(0,2)$ boundary conditions at the boundaries
$\partial (I \times M_2)=M_2 \sqcup M_2$, where $M_2=\mathbb{C}$ or $T^2$. We
introduce supersymmetric indices of three dimensional $\mathcal{N}=2$ theories
on $I \times T^2$ that couple to elliptic genera of 2d $\mathcal{N}=(0,2)$
theories at the two boundaries. We evaluate the $I \times T^2$ indices in terms
of supersymmetric localization and study dualities on the $I \times M_2$. We
consider the dimensional reduction of $I \times T^2$ to $I \times S^1$ and
obtain the localization formula of 2d $\mathcal{N}=(2,2)$ supersymmetric
indices on $I \times S^1$. We illustrate computations of open string Witten
indices based on gauged linear sigma models. Correlation functions of Wilson
loops on $I \times S^1$ agree with Euler pairings in the geometric phase and
also agree with cylinder amplitudes for B-type boundary states of Gepner models
in the Landau-Ginzburg phase.

リンク情報
DOI
https://doi.org/10.1016/j.nuclphysb.2020.115168
arXiv
http://arxiv.org/abs/arXiv:2007.07664
URL
http://arxiv.org/abs/2007.07664v3
URL
http://arxiv.org/pdf/2007.07664v3 本文へのリンクあり

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