Supersymmetry in Hadron Spectroscopy and Solitons in 2 Dimensional Fermionic Media

TL;DR

This paper reviews supersymmetry applications in hadron spectroscopy, superconformal field theory extensions, and soliton dynamics in 2D fermionic media, highlighting recent theoretical developments and their connections to string theory and holography.

Contribution

It presents an overview of supersymmetric approaches to hadron spectroscopy, including superconformal quantum mechanics and holographic QCD, and explores soliton dynamics in 2D fermionic media.

Findings

Spectroscopy of baryons and mesons achieved in light front holographic QCD.

Supersymmetric frameworks connect string theory, gauge theories, and hadron physics.

2D soliton dynamics modeled using quaternionic variables.

Abstract

An overview of hadron spectroscopy obtained from an extension of superconformal field theory of de Alfaro, Fubini and Furlan, which originates from the supergauge transformation of Wess and Zumino and influenced on the string theory are preseted. The standard model of hadron dynamics is based on gauge theory. In the 4 dimensional ($4D$) QCD Lagrangian, the Faddeev-Popov ghost that appears to compensate unphysical degrees of freedom in internal fermion propagators can be regarded as the partner of a fermion. Donaldson formulated a $5D$ gauge theory. Fubini and Rabinovici formulated superconformal quantum mechanics in de Sitter space, and Brodsky and de T\'eramond formulated relativistic light front holographic QCD (LFHQCD) in Kaluza-Klein type $5D$ anti de Sitter (AdS) space, using Dirac's light cone gauge, and succeeded in obtaining spectroscopy of baryons (fermions) and corresponding mesons (bosons), except the pion which is an axial scalar meson that remains massless. In the LFHQCD, the time parameter $\tau=t\pm z/c$, $(z\in {\bf C})$ appears by the choice of the light-cone gauge, or the front form of Dirac's formulation. The theory is an extension of AdS/CFT correspodence of Maldacena in which incorporation of Einstein's gravity theory in Maxwell's electromagnetic theory was tried in the framework of the string theory. Taking mathematical frameworks of treating the supersymmetry by Brodsky, Witten, Connes and their collaborators as central thema, we summarize other supersymmetric approaches like string theory in particle physics and astrophysics. We discuss about 2 dimensional solitons whose dynamics is represented also by $\tau=t\pm z/c$, ($z\in$ pure quaternion${\bf H}$).