A Note on Effective String Theory

TL;DR

This paper introduces a toy model for an effective string theory in higher-dimensional target spaces, demonstrating well-behaved scaling exponents and exploring its potential relevance to the infrared behavior of Yang-Mills theory.

Contribution

It proposes a simplified model for random surfaces in higher dimensions, providing insights into effective string descriptions of gauge theories.

Findings

Scaling exponents are well-behaved in the model.

The toy model offers useful perspectives on effective string theories.

Potential relevance to infrared limits of Yang-Mills theory.

Abstract

Motivated by the possibility of an effective string description for the infrared limit of pure Yang-Mills theory, we present a toy model for an effective theory of random surfaces propagating in a target space of $D>2$. We show that the scaling exponents for the fixed area partition function of the theory are apparently well behaved. We make some observations regarding the usefulness of this toy model.