3D Yang-Mills Glueballs vs Closed Effective Strings

TL;DR

This paper compares the Axionic String Ansatz for 3D Yang-Mills glueballs, modeled as closed strings, with effective string theory predictions, confirming some key features and highlighting discrepancies at higher excitations.

Contribution

It provides a detailed comparison between ASA and effective string theory spectra for glueballs, elucidating their agreement near the leading Regge trajectory and discrepancies at higher states.

Findings

Effective string theory correctly predicts even spin glueballs on the leading Regge trajectory.

The spectrum matches ASA predictions near the leading Regge trajectory.

Effective string theory overestimates glueball states far above the leading Regge trajectory.

Abstract

Recent lattice results strongly support the Axionic String Ansatz (ASA) for quantum numbers of glueballs in 3D Yang-Mills theory. The ASA treats glueballs as closed bosonic strings. The corresponding worldsheet theory is a deformation of the minimal Nambu-Goto theory. In order to understand better the ASA strings and as a first step towards a perturbative calculation of the glueball mass splittings we compare the ASA spectrum to the closed effective string theory. Namely, we model glueballs as excitations around the folded rotating rod solution with a large angular momentum $J$. The resulting spectrum agrees with the ASA in the regime of validity of the effective theory, i.e., in the vicinity of the leading Regge trajectory. In particular, closed effective string theory correctly predicts that only glueballs of even spin $J$ show up at the leading Regge trajectory. Interestingly though, the closed effective string theory overestimates the number of glueball states far above the leading Regge trajectory.