超弦场论、超场与超几何
Superstring Field Theory, Superforms and Supergeometry
摘要：
受超弦场论的启发，我们从层理论的角度研究了超流形上的微分、积分和逆形式及其相互关系。特别是，在这种情况下，在几何的方式恢复的积分形式的形式分布特性。此外，我们还展示了逆形式如何在超流形上扩展普通的德拉姆复形，从而为超弦中使用的大希尔伯特空间提供了数学基础。最后，我们简要地讨论了如何霍奇钻石的超流形看起来像，我们明确地计算它的超黎曼曲面。
英文摘要：
Inspired by superstring field theory, we study differential, integral, and inverse forms and their mutual relations on a supermanifold from a sheaf-theoretical point of view. In particular, the formal distributional properties of integral forms are recovered in this scenario in a geometrical way. Further, we show how inverse forms extend the ordinary de Rham complex on a supermanifold, thus providing a mathematical foundation of the Large Hilbert Space used in superstrings. Last, we briefly discuss how the Hodge diamond of a supermanifold looks like, and we explicitly compute it for super Riemann surfaces.
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