Yang-Mills glueballs as closed bosonic strings

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.

Asymptotic fragility, near AdS2 holography and T T ¯ $$ T\overline{T} $$

“…After the full symmetry is identified it should be possible to evaluate the partition function in the long string sector (in analogy to section 4) and also to extend this analysis to short strings 11 (similarly to the critical string case [27]). This may open the path to put on a solid footing the heuristic analysis of the D = 3 glueball spectrum presented in [20]. A rather surprising outcome of [20] is that glueball quantum numbers apparently all can be determined by the semiclassical ansatz, which a priori is expected to work only in the large spin limit.…”

“…This may open the path to put on a solid footing the heuristic analysis of the D = 3 glueball spectrum presented in [20]. A rather surprising outcome of [20] is that glueball quantum numbers apparently all can be determined by the semiclassical ansatz, which a priori is expected to work only in the large spin limit. If confirmed, this surprising effectiveness of semiclassics may be yet another indication that the partition function for (5.1) exhibits the localization property, similarly to section 4.…”

“…In the Polyakov description this setup is especially similar to the one encountered in the JT gravity: in addition to transverse fields X i , representing propagating physical modes, one finds an additional topological sector consisting of the Polyakov metric and X 0,1 , whose only role is to provide a dynamical set of coordinates. A detailed derivation of the worldsheet S-matrix in the Polyakov formalism 3 is presented in [20]. Let us see what happens if one treats the JT gravity in a similar way.…”

“…Intriguingly, the TBA analysis [35,36] of the available lattice data in D = 3 and D = 4 gluodynamics [37][38][39] suggests that confining strings may be described as deformations of these simple integrable models -leading to the Axionic String Ansatz (ASA) [20,34]. Up until now a theoretical development of the ASA was largely impeded by the absence of a tractable path integral formalism to describe gravitational dressing.…”

Glueball spins in D = 3 Yang-Mills

“…At D = 3 these are glueball spin J, spatial parity P and charge conjugation parity C. J > 0 glueball states come out as doublets of states carrying opposite spatial parities P , so that P carries non-trivial information only for J = 0 glueballs. We will refer to the resulting spectrum as the ASA spectrum, but it is important to keep in mind that some additional assumptions have been made in [17], which may be not a part of the ASA.…”