Finite Strings From Non-Chiral Mumford Forms

TL;DR

This paper constructs an infinite class of singularity-free partition functions on the moduli space of Riemann surfaces, involving specific world-sheet systems and derived from Mumford forms, advancing string theory mathematical foundations.

Contribution

It introduces a new class of partition functions free of boundary singularities, derived from Mumford forms mapped to scalar forms on the moduli space, expanding the understanding of string world-sheet models.

Findings

Partition functions are free of singularities at the Deligne-Mumford boundary.

Constructed from specific world-sheet systems including $b$-$c$ and beta-gamma systems.

Derived from mapping Mumford forms to scalar forms on the moduli space.

Abstract

We show that there is an infinite class of partition functions with world-sheet metric, space-time coordinates and first order systems, that correspond to volume forms on the moduli space of Riemann surfaces and are free of singularities at the Deligne-Mumford boundary. An example is the partition function with 4=2(c_2+c_3+c_4-c_5) space-time coordinates, a $b$-$c$ system of weight 3, one of weight 4 and a beta-gamma system of weight 5. Such partition functions are derived from the mapping of the Mumford forms to non-factorized scalar forms on M_g introduced in arXiv:1209.6049.