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

Katsuyuki Sugiyama; Yutaka Yoshida

doi:10.1016/j.nuclphysb.2020.115168

paper

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

arXiv:2007.07664 · doi:10.1016/j.nuclphysb.2020.115168

Abstract

We study three dimensional $N = 2$ supersymmetric theories on $I \times M_{2}$ with 2d $N = (0, 2)$ boundary conditions at the boundaries $\partial (I \times M_{2}) = M_{2} ⊔ M_{2}$ , where $M_{2} = C$ or $T^{2}$ . We introduce supersymmetric indices of three dimensional $N = 2$ theories on $I \times T^{2}$ that couple to elliptic genera of 2d $N = (0, 2)$ 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 $N = (2, 2)$ 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.

54 pages, minor changes

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

Abstract

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Supersymmetric indices on I×T2, elliptic genera and dualities with boundaries

Abstract

References in corpus (6)

Cited by in corpus (8)

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