2001/10/31 by Eric D'Hoker, Eric D’Hoker, D. H. Phong · 11 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Particle physics theoretical and experimental studies #hep-th #math.CV
paper · pdf · doi:10.1016/s0370-2693(02)01255-8
published as Phys.Lett.B529:241-255,2002 · 21 pages, no figures, references added, minor typos corrected
arxiv created 2001/12/24 · openalex publication_date 2002/03/01 · arxiv updated 2009/11/30 · openalex created_date 2022/08/13 · openalex updated_date 2026/07/30
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.