Discretized Light-Cone Quantization of Two-Dimensional SU\((N)\) Gauge Theories

Abstract

This thesis studies two ((1+1))-dimensional theories of quantum chromodynamics with gauge group (\mathrm{SU}(N)). The first theory, (\mathcal{T}), consists of (N_\mathrm{adj}) flavors of gluinos and one massive quark. The second theory, (\mathcal{T}'), consists of (N_\mathrm{fund}) massless quarks and one massive quark. We use a method called discretized light-cone quantization (DLCQ) to find the mass spectra of these theories numerically. At large (N), we use a mathematical correspondence between (\mathcal{T}) and (\mathcal{T}') to indirectly compute the height of the quark-antiquark interaction potential in (\mathcal{T}) for the case of zero gluino mass. We show that, to first order in (1/N_\mathrm{adj}), this numerical result agrees with a perturbative Wilson loop calculation. We extend the Wilson loop calculation to massive gluinos, demonstrating that the theory transitions to a confining phase as the gluino mass is turned on. Finally, we consider the more difficult case of (N=2). We restrict to the pure gluino theory and develop new techniques based on (\mathfrak{su}(2)) representation theory to vastly improve the efficiency of the numerics. Our results show that, when the gluino mass is (m^2_\mathrm{adj}=2,g^2/\pi), the bosonic and fermionic spectra approach the same values in the continuum limit, which is the first numerical evidence for supersymmetry at finite (N).