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Geometry of fermionic string. (English) Zbl 0751.53024

Proc. Int. Congr. Math., Kyoto/Japan 1990, Vol. II, 1377-1386 (1991).
[For the entire collection see Zbl 0741.00020.]
This paper is a concise review of previous work by the author [e.g. Nucl. Phys. B 317, 323-343 (1989)] and various collaborators on superconformal geometry, which has its physical roots in the Polyakov description of the fermionic string. Among the topics covered are the origin of the string measure on superconformal moduli space and analytic properties of this measure, the construction of universal moduli space and the expression of the string measure in terms of the super \(\tau\)-function. The results concerning the measure on the moduli space of \(N=2\) superconformal manifolds are new.
Reviewer: H.Rumpf (Wien)

MSC:

53Z05 Applications of differential geometry to physics
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory