Lattice Determination of the Baryon Junction Mass in $(2+1)$ Dimensions

This contribution investigates baryonic flux tube configurations in $SU(3)$ Yang–Mills theory in $(2+1)$ dimensions. Leveraging recent next-to-leading-order results within the Effective String Theory (EST) framework, which explicitly include corrections proportional to the baryon junction mass $M$ up to order $1\mathrm{/}{R}^2$, we carry out a non-perturbative determination of this parameter, through high-precision simulations of the three-point Polyakov-loop in the open string channel. In addition, the high-temperature regime of the baryonic system is examined in order to test the Svetitsky–Yaffe conjecture. Close to the deconfinement transition, the lattice results for the correlators show close agreement with the predictions of the two-dimensional three-state Potts model.