Supersymmetric localization of refined chiral multiplets on topologically twisted \(H^2 \times S^1\). (English) Zbl 1435.81222
Summary: We derive the partition function of an \(\mathcal{N} = 2\) chiral multiplet on topologically twisted \(H^2 \times S^1\). The chiral multiplet is coupled to a background vector multiplet encoding a real mass deformation. We consider an \(H^2 \times S^1\) metric containing two parameters: one is the \(S^1\) radius, while the other gives a fugacity \(q\) for the angular momentum on \(H^2\). The computation is carried out by means of supersymmetric localization, which provides a finite answer written in terms of \(q\)-Pochammer symbols and multiple Zeta functions. Especially, the partition function of normalizable fields reproduces three-dimensional holomorphic blocks.
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 81R25 | Spinor and twistor methods applied to problems in quantum theory |
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