Work

RNS superstring measure for genus 3

Year: 2025

Type: article

Abstract: A bstract We propose a new formula for the RNS superstring measure for genus 3. Our derivation is based on invariant theory. We follow Witten’s idea of using an algebraic parametrization of the moduli space (which he applied to re-derive D’Hoker and Phong’s formula for the RNS superstring measure for genus 2); but the particular parametrization that we use has not been applied to superstring theory before. We prove that the superstring measure is a linear combination (with complex coefficients) of three known functions. Furthermore, we conjecture the values of the coefficients of this linear combination and provide evidence for this conjecture. Unlike the Ansatz of Cacciatori, Dalla Piazza and van Geemen from 2008, our formula has a polar singularity along the hyperelliptic locus; the existence of this singularity was established by Witten in 2015. Moreover, our formula is not an Ansatz but follows from first principles, except for the values of the three coefficients.

Source: Journal of High Energy Physics

DOI: 10.1007/jhep10(2025)193

Authors: P. Dunin-Barkowski, I. Fedorov, A. Sleptsov

Institutions: National Research University Higher School of Economics, Skolkovo Institute of Science and Technology, Kurchatov Institute, Moscow Institute of Physics and Technology, Institute for Information Transmission Problems

Language: English

Topic: Black Holes and Theoretical Physics

Subfield: Nuclear and High Energy Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

Funders: National Research University Higher School of Economics, Ministry of Science and Higher Education of the Russian Federation

Award: G2622452862