Confinement and Pseudoscalar Glueball Spectrum in the 2 + 1D QCD-Like Theory from the Non-Susy D2 Brane

Adrita Chakraborty,A Rothkopf,D Röhrich,L Tolos,A Kurkela,N Brambilla,J.O Andersen,A Tranberg,K Tywoniuk

doi:10.1051/epjconf/202225810004

Abstract

We study two important properties of 2+1D QCD, namely confinement and Pseudoscalar glueball spectrum, using holographic approach. The confined state of the bounded quark-antiquark pair occurs in the self-coupling dominated nonperturbative regime, where the free gluons form the bound states, known as glueballs. The gauge theory corresponding to low energy decoupled geometry of isotropic non-supersymmetric D2 brane, which is again similar to the 2+1D YM theory, has been taken into account but in this case the coupling constant is found to vary with the energy scale. At BPS limit, this theory reduces to supersymmetric YM theory. We have considered NG action of a test string and calculate the potential of such confined state located on the boundary. The QCD flux tube tension for large quark-antiquark separation is observed to be a monotonically increasing function of running coupling. The mass spectrum of Pseudoscalar glueball is evaluated numerically from the fluctuations of the axion in the gravity theory using WKB approximation. This produces the mass to be related to the string tension and the levels of the first three energy states. The various results that we obtained quite match with those previously studied through the lattice approach.

Highlights

Unlike the four dimensional theory, the three dimensional Yang-Mills theory having the dimension-full coupling g2YM is not classically scale-invariant
The mass spectrum of Pseudoscalar glueballs in the 2+1D pure YM theory from the Schrödinger-like field equation of the axion’s fluctuation using the WKB approximation
We evaluate the ratio M0−+ / σ for n = 0, 1, 2 states in the complete non-perturbative region [9] and this put forth an emperical relation of pseudoscalar glueball masses to the QCD flux-tube tension as 103 √ 6 3π3

Summary

Introduction

Unlike the four dimensional theory, the three dimensional Yang-Mills theory having the dimension-full coupling g2YM is not classically scale-invariant. For large Nc, 2 + 1 dimensional pure YM theory is theoretically found to have QCD flux-tube tension [6], σ This confinement indicates strong self-coupling dominated regime where the free gluons form the bound states, called glueballs. Its discrete energy spectrum or mass gap in the confined phase We study these two properties of the 2 + 1 dimensional non-perturbative QCD with the holographic approach. To ensure of the strong coupling nonperturbative behaviour in the gauge theory side the number of D-branes, Nc, living on the boundary of the bulk is taken to be Nc → ∞ This duality has been proved to be an effective technique to unravel non-perturbative non-conformal QCD-like theories by dragging it to some gravity dual on non-AdS background. The mass spectrum is evaluated numerically but the restrictions in the WKB method constrained us in the lower states only

Non-Susy D2 Brane

Decoupled Geometry

Confinement

2: Dependence of um u2 with δ and the δ-dependence of QCD string tension

Conclusion