Yang--Mills Glueballs as Closed Bosonic Strings

TL;DR

The paper introduces the Axionic String Ansatz (ASA) as a unified description of confining-string dynamics in Yang–Mills theories in $D=3$ and $D=4$, positing an integrable axionic worldsheet with minimal local degrees of freedom (no extra massless fields in $D=3$, a worldsheet axion in $D=4$). By combining a tensor-square structure for closed strings, level-matching constraints, and an open-string-like semiclassical spectrum, the authors derive concrete predictions for the quantum numbers (spins, $P$- and $C$-parities) of glueballs. They confront these predictions with lattice data in 3D, finding encouraging agreement for the first four levels and proposing reassignments to maintain the tensor-square pattern, while noting that 4D data point toward a worldsheet axion consistent with long-string analyses. The work argues that a string-based description of the glueball spectrum is viable and outlines a program to obtain quantitative spectrum corrections around the integrable ASA and to address remaining puzzles, such as a potential Regge-slope discrepancy and the spins of higher states.

Abstract

We put forward the Axionic String Ansatz (ASA), which provides a unified description for the worldsheet dynamics of confining strings in pure Yang--Mills theory both in $D=3$ and $D=4$ space-time dimensions. The ASA is motivated by the excitation spectrum of long confining strings, as measured on a lattice, and by recently constructed integrable axionic non-critical string models. According to the ASA, pure gluodynamics in 3D is described by a non-critical bosonic string theory without any extra local worldsheet degrees of freedom. We argue that this assumption fixes the set of quantum numbers (spins, $P$- and $C$-parities) of almost all glueball states. We confront the resulting predictions with the properties of approximately $1^2+2^2+3^2+5^2=39$ lightest glueball states measured on a lattice and find a good agreement. On the other hand, the spectrum of low lying glueballs in 4D gluodynamics suggests the presence of a massive pseudoscalar mode on the string worldsheet, in agreement with the ASA and lattice data for long strings.

Figures (6)

• Figure 1: Glueball production in the worldsheet scattering proceeds through string intersection and interconnection. At large $N_c$ the probability of interconnection is suppressed by $1/N_c^2$.
• Figure 2: Helicity content of the ASA open string spectrum.
• Figure 3: 3D glueball spectrum and quantum numbers as measured on a lattice.
• Figure 4: Measured 3D glueball spectrum with the ASA quantum numbers assignments. The dashed line shows the approximately linear leading Regge trajectory.
• Figure 5: 4D glueball spectrum and quantum numbers.