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I am reading Vafa's paper 'Topological Mirros and Quantum Strings'(arXiv:hep-th/9111017). In this paper, the author says the Hilbert Space of a fermionic string theory corresponds to the space of semi-infinite forms on the loop space.

I only know differential forms (of non-negative degrees) before so I would like to know is there some nice introduction material to this kind of 'semi-infinite form', which can also have negative degrees?

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