2017/09/30 by Akihiro Tsuchiya, Tsuchiya, A. G.
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · pdf · doi:10.48550/arxiv.1710.00206
openalex publication_date 2017/09/30 · openalex created_date 2017/10/20 · openalex updated_date 2026/07/28
Theta identities on genus g Riemann surfaces which decompose simple products of fermion correlation functions with a constraint on their variables are considered. This type of theta identities is, in a sense, dual to Fay s formula, by which it is possible to sum over spin structures of certain part of superstring amplitudes in NSR formalism without using Fay s formula nor Riemann s theta formula in much simpler, more transparent way. Also, such identities will help to cast correlation functions among arbitrary numbers of Kac-Moody currents in a closed form. As for genus 1, the identities are reported before in ref[1] [2]. Based on some notes on genus 1 case which were not reported in ref[1] [2] and relating those to the results of the Dolan Goddard method ref[3] on describing Kac-Moody currents in a closed form, we propose an idea of generalizing genus 1 identities to the case of genus g surfaces. This is not a complete derivation of the higher genus formula due to difficulties of investigating singular part of derivatives of genus g Weierstrass Pe functions. Mathematical issues remained unsolved for genus g >1 are described in the text.