Partition functions of N=1 gauge theories on S2×R2ε and duality

Taro Kimura (1, 2) , Jun Nian (3, 4) , Peng Zhao (5)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]
2 Department of Physics, Faculty of Science and Technology, Keio University
3 Leinweber Center for Theoretical Physics [University of Michigan]
4 Riemann Center for Geometry and Physics, Leibniz University Hannover
5 Institute of Theoretical Physics China

We compute the partition functions of N=1 gauge theories on S2×R2ε using supersymmetric localization. The path integral reduces to a sum over vortices at the poles of S2 and at the origin of R2ε. The exact partition functions allow us to test Seiberg duality beyond the supersymmetric index. We propose the N=1 partition functions on the Ω-background, and show that the Nekrasov partition functions can be recovered from these building blocks.

Mots clés: Supersymmetry; N=1 supersymmetry; supersymmetric gauge theory; supersymmetric localization; partition function; vortex; Seiberg duality; Nekrasov partition function

Domaines: Mathématiques [math]

Taro Kimura, Jun Nian, Peng Zhao. Partition functions of N=1 gauge theories on S2×R2ε and duality. International Journal of Modern Physics A, 2020, 35 (33), pp.2050207. ⟨10.1142/S0217751X20502073⟩. ⟨hal-03046726⟩