On the full bosonic string from Minkowski space to Riemannian manifolds

TL;DR

This paper explores the full bosonic string action with a Minkowski domain and Riemannian target, analyzing the coupled wave map equations with potentials and proving existence results for solutions.

Contribution

It introduces the study of the full bosonic string in this setting and establishes existence results for the coupled equations, advancing understanding of their mathematical properties.

Findings

Analysis of the coupled wave map and potential equations

Existence results for solutions of the string equations

Insights into the mathematical structure of the bosonic string

Abstract

We study the action of the full bosonic string for the domain being two-dimensional Minkowski space and the target a Riemannian manifold. Its critical points couple the wave map equation to a scalar and a two-form potential. Besides investigating their basic features we establish existence results for the latter.