Confining Strings in a Gapless Phase

TL;DR

This paper investigates the quantum properties of confining strings in a gapless four-dimensional theory, revealing deviations from standard Effective String Theory and exploring their connection to flux configurations in UV completions.

Contribution

It provides a detailed analysis of finite-tension string solutions, quantum corrections, and conditions under which EST predictions are recovered in a gapless 4D model.

Findings

Quantum corrections to string energy and width are computed.

Deviations from universal EST predictions are identified.

Connections to stable fluxes in UV completions are discussed.

Abstract

We consider the dynamics of confined strings embedded in a gapless four-dimensional theory. To this end, we examine finite-tension string-like solutions to the equations of motion of the $\mathbb{C}\mathbb{P}^1$ non-linear sigma model. We present a comprehensive analysis of the quantum fluctuations around these solutions and derive the corresponding spectrum. These results allow us to determine the quantum corrections to the closed string ground state energy in both the finite- and infinite-size limits. Furthermore, we analyze quantum corrections to the string's effective width. We find that these observables generically depart from the universal predictions of standard Effective String Theory (EST), and we identify specific limits in which the bulk dynamics decouple and EST is recovered. Finally, we discuss the connection between these string configurations and stable electric and magnetic fluxes arising in certain ultraviolet completions of the $\mathbb{C}\mathbb{P}^1$ model.