Towards an effective string theory for the flux-tube spectrum

Parallel talk presented at the Lattice 2024 conference in Liverpool. 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 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. 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 should accompany the Nambu-Goto framework. In our presentation, we will provide compelling evidence that this approach can closely approximate the flux-tube data. We will demonstrate this by comparing results obtained for the spectrum of the closed $SU(N)$ flux-tube using lattice techniques in four dimensions.