Automorphism Group of $k((t))$: Applications to the Bosonic String

TL;DR

This paper develops a non-perturbative framework for bosonic string theory using a formal group that links Virasoro algebra representations with moduli spaces of curves, revealing new structural insights.

Contribution

It introduces a formal group acting as a universal moduli space connecting Virasoro representations and curve moduli, with a local Mumford formula application.

Findings

Established a formal group G as a universal moduli space.

Linked Virasoro algebra representations to moduli of curves.

Proved a local Mumford formula on G.

Abstract

This paper is concerned with the formulation of a non-pertubative theory of the bosonic string. We introduce a formal group $G$ which we propose as the ``universal moduli space'' for such a formulation. This is motivated because $G$ establishes a natural link between representations of the Virasoro algebra and the moduli space of curves. Among other properties of $G$ it is shown that a ``local'' version of the Mumford formula holds on $G$.