2001/11/05 by Eric D'Hoker, Eric D’Hoker, D. H. Phong · 5 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-th #math.CV
paper · pdf · doi:10.1016/s0550-3213(02)00516-3
published as Nucl.Phys.B639:129-181,2002 · 58 pages, no figures
arxiv created 2001/11/05 · openalex publication_date 2002/09/01 · arxiv updated 2009/11/30 · openalex created_date 2022/08/13 · openalex updated_date 2026/04/05
The slice-independent gauge-fixed superstring chiral measure in genus 2 derived in the earlier papers of this series for each spin structure is evaluated explicitly in terms of theta-constants. The slice-independence allows an arbitrary choice of superghost insertion points q1, q2 in the explicit evaluation, and the most effective one turns out to be the split gauge defined by Sδ(q1,q2)=0. This results in expressions involving bilinear theta-constants M. The final formula in terms of only theta-constants follows from new identities between M and theta-constants which may be interesting in their own right. The action of the modular group Sp(4,Z) is worked out explicitly for the contribution of each spin structure to the superstring chiral measure. It is found that there is a unique choice of relative phases which insures the modular invariance of the full chiral superstring measure, and hence a unique way of implementing the GSO projection for even spin structure. The resulting cosmological constant vanishes, not by a Riemann identity, but rather by the genus 2 identity expressing any modular form of weight 8 as the square of a modular form of weight 4. The degeneration limits for the contribution of each spin structure are determined, and the divergences, before the GSO projection, are found to be the ones expected on physical grounds.