标题： RNS 超弦测度 3 阶曲面 显示英文标题

标题： RNS superstring measure for genus 3

摘要： 我们提出了一个关于3类的RNS超弦测度的新公式。 我们的推导基于不变式理论。 我们遵循维滕使用模空间的代数参数化的思想（他将其应用于重新推导D'Hoker和Phong关于2类的RNS超弦测度的公式）；但我们使用的特定参数化以前从未应用于超弦理论。 我们证明了超弦测度是三个已知函数的线性组合（具有复系数）。 此外，我们猜测了这个线性组合的系数值，并提供了对此猜测的证据。 与Cacciatori、Dalla Piazza和van Geemen在2008年的假设不同，我们的公式在双曲椭圆轨迹上具有极点奇异性；这种奇异性存在的事实由维滕在2015年确立。 此外，我们的公式不是假设，而是从基本原理推导出来的，除了三个系数的值外。 显示英文摘要

摘要： We propose a new formula for the RNS supersting 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 combinaition (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.