Probing boundary-corrections to Nambu-Goto open string energy levels in 3d SU(2) gauge theory

TL;DR

This study measures the energy levels of flux tube excitations in 3D SU(2) gauge theory, finding boundary correction effects to Nambu-Goto string predictions, especially impacting excited states.

Contribution

It provides the first lattice measurement of boundary corrections to Nambu-Goto string energy levels in 3D SU(2) gauge theory, including excited states.

Findings

Boundary corrections appear at order 1/R^4.

Coefficient of boundary correction term is approximately -0.5.

Excited states show larger deviations from Nambu-Goto predictions.

Abstract

We measure the energy levels of the excitations of the flux tube between static quark and antiquark in three-dimensional SU(2) gauge theory. Combining exponential error reduction techniques and a variational method we are able to reduce the errors for the excited states significantly and to extract excited states in distinct parity and charge conjugation channels. It is conjectured that the infrared behavior (at large q\bar{q} separation R) of the flux tube is governed by an effective string theory. Indeed previous simulations show good agreement between lattice data and predictions from Nambu-Goto string theory. Recently, new results on the effective string theory obtained corrections to the Nambu-Goto predictions and showed that for the open string in three dimensions first corrections should appears at order 1/R^4. They correspond to boundary terms in the worldsheet field theory. These corrections are presumably small for the ground state, but significantly larger for the excited states and lift the degeneracies of the free theory. Assuming this functional form of the correction, we obtain for the coefficient b_2=-0.5(2)(2).