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arXiv 2012.119612020-12-22math-phmath.AGmath.MP

Hyperbolic Superspaces and Super-Riemann Surfaces

Zhi Hu, Runhong Zong

发表信息：: Communications in Mathematical Physics, Volume 378, Number 2, pp 891-915 (2020)
DOI：: 10.1007/s00220-020-03801-5

英文摘要：

In this paper, we will generalize some results in Manin's paper "Three-dimensional hyperbolic geometry as $\infty$-adic Arakelov geometry" to the supergeometric setting. More precisely, viewing $\mathbb{C}^{1|1}$ as the boundary of the hyperbolic superspace $\mathcal{H}^{3|2}$, we reexpress the super-Green functions on the supersphere $\hat{\mathbb{C}}^{1|1}$ and the supertorus $T^{1|1}$ by some data derived from the supergeodesics in $\mathcal{H}^{3|2}$.

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