Immersions and folds in string theories of gauge fields

TL;DR

This paper introduces a two-dimensional string model with a self-intersection term in the action, exploring its implications for gauge fields and the conditions for fold cancellation, linking 2D models to 4D theories.

Contribution

It presents a novel string model incorporating self-intersection numbers and analyzes fold cancellation, connecting 2D string dynamics with 4D gauge theories.

Findings

Self-intersection number defined for immersed surfaces in 4D

Fold cancellation enforces the string θ angle to be π

Constructed candidate string states and provided mathematical background

Abstract

A two-dimensional string model with dynamical cancellation of folds is considered. The action of the model contains the self-intersection number which is defined for surfaces immersed into 4D targets. The two additional variables are not dynamical and live on a compact manifold. In this sense the model is a compactification of a 4D theory. The cancellation forces the string $\th$ angle to be equal $\pi$. Candidates for string states are constructed. Some mathematical background is given.