Adjoint Majorana QCD${}_2$ at Finite $N$

Abstract

The mass spectrum of $1+1$-dimensional $\mathrm{SU}(N)$ gauge theory coupled to a Majorana fermion in the adjoint representation has been studied in the large $N$ limit using Light-Cone Quantization. Here we extend this approach to theories with small values of $N$, exhibiting explicit results for $N=2,3$, and $4$. In the context of Discretized Light-Cone Quantization, we develop a procedure based on the Cayley-Hamilton theorem for determining which states of the large $N$ theory become null at finite $N$. For the low-lying bound states, we find that the squared masses divided by $g^{2}N$, where $g$ is the gauge coupling, have very weak dependence on $N$. The coefficients of the $1/N^2$ corrections to their large $N$ values are surprisingly small. When the adjoint fermion is massless, we observe exact degeneracies that we explain in terms of a Kac-Moody algebra construction and charge conjugation symmetry. When the squared mass of the adjoint fermion is tuned to $g^{2}N/\pi$, we find evidence that the spectrum exhibits boson-fermion degeneracies, in agreement with the supersymmetry of the model at any value of $N$.

45 pages, 7 figures

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Cited by in corpus (5)

• Effective Hamiltonians and Counterterms for Hamiltonian Truncation
• 2d QCD and Integrability, Part I: 't Hooft model
• Comments on 1+1d QCD with heavy adjoint quarks
• $1/N$ Corrections in ${\text{QCD}}_2$: Small Mass Limit and Threshold States
• RG Flows in 2d Chiral Gauge Theories