Two-loop superstrings.: I. Main formulas

By E. D’Hoker, Duong H. Phong. 2001

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Abstract An unambiguous and slice-independent formula for the two-loop superstring measure on moduli space for even spin structure is constructed from first principles. The construction uses the super-period matrix as moduli invariant under worldsheet supersymmetry. This produces new subtle contributions to the gauge-fixing process, which eliminate all the ambiguities plaguing earlier gauge-fixed formulas. The superstring measure can be computed explicitly and a simple expression in terms of modular forms is obtained. For fixed spin structure, the measure exhibits the expected behavior under degenerations of the surface. The measure allows for a unique modular covariant GSO projection. Under this GSO projection, the cosmological constant, the 1-, 2- and 3-point functions of massless supergravitons all vanish pointwise on moduli space without the appearance of boundary terms. A certain disconnected part of the 4-point function is shown to be given by a convergent, finite integral on moduli space. A general slice-independent formula is given for the two-loop cosmological constant in compactifications with central charge c =15 and N =1 worldsheet supersymmetry in terms of the data of the compactification conformal field theory. In this Letter, a summary of the above results is presented with detailed constructions, derivations and proofs to be provided in a series of subsequent publications.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/540326c8d16fa8a00efb0835d577c4b0f96288d5