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arXiv · 1611.04804

N=2 gauge theories on the hemisphere $HS^4$

Edi Gava·K. S. Narain·Nouman Muteeb·V. I. Giraldo-Rivera
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Abstract

Using localization techniques, we compute the path integral of $N=2$ SUSY gauge theory coupled to matter on the hemisphere $HS^4$, with either Dirichlet or Neumann supersymmetric boundary conditions. The resulting quantities are wave-functions of the theory depending on the boundary data. The one-loop determinant are computed using $SO(4)$ harmonics basis. We solve kernel and co-kernel equations for the relevant differential operators arising from gauge and matter localizing actions. The second method utilizes full $SO(5)$ harmonics to reduce the computation to evaluating $Q_{SUSY}^2$ eigenvalues and its multiplicities. In the Dirichlet case, we show how to glue two wave-functions to get back the partition function of round $S^4$. We will also describe how to obtain the same results using $SO(5)$ harmonics basis.

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Edi Gava, K. S. Narain, Nouman Muteeb, V. I. Giraldo-Rivera. 2016-11-15. N=2 gauge theories on the hemisphere $HS^4$. https://doi.org/10.1016/j.nuclphysb.2017.04.007

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