Confining strings in a gapless phase

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 ℂ 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. We find that the leading corrections beyond the EST regime scale logarithmically with the string length, providing a smoking gun of the interactions with a gapless bulk. 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 ℂ ℙ 1 model.