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Recently Grinstein, Jora, and Polosa have studied a theory of large-$N$scalar quantum chromodynamics in one-space one-time dimension. This theoryadmits a Bethe-Salpeter equation describing the discrete spectrum ofquark-antiquark bound states. They consider gauge fields in the adjointrepresentation of $SU(N)$ and scalar fields in the fundamental representation.The theory is asymptotically free and linearly confining. The theory couldpossibly provide a good field theoretic framework for the description of alarge class of diquark-antidiquark (tetra-quark) states. Recently we havestudied the light-front quantization of this theory without a Higgs potential.In the present work, we study the light-front Hamiltonian, path integral andBRST formulations of the theory in the presence of a Higgs potential. Thelight-front theory is seen to be gauge-invariant, possessing a set offirst-class constraints. The explicit occurrence of spontaneous symmetrybreaking in the theory is shown in unitary gauge as well as in the light-front't Hooft gauge.

Hamiltonian, Path Integral and BRST Formulations of Large N Scalar $QCD_{2}$ on the Light-Front and Spontaneous Symmetry Breaking