Towards an Effective String Theory for the flux tube

TL;DR

This paper proposes an improved effective string theory for the confining flux tube, combining a Thermodynamic Bethe Ansatz approach with an axion field component, to better match lattice data and explain excitation deviations.

Contribution

It introduces a novel effective string model incorporating TBA analysis and an axion field, advancing the understanding of flux tube spectra beyond the traditional Nambu-Goto framework.

Findings

TBA analysis yields a robust flux-tube spectrum model.

Lattice data supports the existence of an axion field on the flux tube.

The combined approach closely matches lattice results for SU(N_c) flux tubes.

Abstract

The quest to develop an effective string theory capable of describing the confining flux tube has been a longstanding objective within the theoretical physics community. Recent lattice results indicate that the low-lying spectrum of the flux tube in both three and four dimensions can be partially described by the Nambu-Goto string with minor deviations. However, several excitation states exhibit significant corrections that have remained unexplained until recently. Recent advancements suggest that a Thermodynamic Bethe Ansatz (TBA) analysis, expanded in both $1/R \sqrt{\sigma}$ and the softness of phonons i.e. $p/\sqrt{\sigma}$, can lead to a robust effective string theory for the flux-tube with length $R$. Furthermore, lattice data points to the existence of an axion field on the world-sheet of the flux-tube, implying that an Axionic String Ansatz (ASA) should accompany the Nambu-Goto framework. We will provide compelling evidence in these proceedings that this approach can closely approximate the flux tube data. We will demonstrate this by comparing results obtained for the spectrum of the closed $SU(N_c)$ flux-tube extracted using lattice techniques in four dimensions.