Excitations of torelon

TL;DR

The paper investigates excitations of the QCD flux tube (torelon) in SU(3) Yang–Mills theory using anisotropic lattice simulations and a rich operator basis projected onto longitudinal momentum $p_z$ and transverse lattice irreps. Energies are extracted from exponential decays of correlation functions, with a variational method optimizing overlaps among eight prototype paths on lattices of extent $L_z=8$–$16 a_s$ and anisotropy $a_s/a_t=6$. The results are compared to effective string theories, notably the Nambu-Goto and Polchinski-Strominger frameworks, finding that leading energy gaps follow $E_N \approx 2\pi N / L$ while the fine structure depends on $p_z$ and exhibits nontrivial degeneracy patterns that evolve with $L$. These findings support a string-like description of long torelons while highlighting challenges in predicting the detailed spectrum, underscoring the need for continuum extrapolation and exploration with larger torelons. $2\pi N / L$ is a key scaling relation identified in the data.

Abstract

The excitations of gluonic flux tube in a periodic lattice are examined. Monte Carlo simulations from an anisotropic lattice are presented and the comparison with effective string models is discussed.

Figures (2)

• Figure 1: The eight prototype lattice paths used in the construction of torelon operators in this work.
• Figure 2: Energies of torelons of different lengths. The solid lines are the first order string prediction, $2\pi N/L$.