Renormalization group flow of QCD in 1+1 Dimensions

This work presents first stages of studying two-dimensional Quantum Chromodynamics with the Functional Renormalization Group. The model is studied in the vacuum and two truncations of different complexity are made for the effective average action where the regularization is implemented by Callan-Symanzik type regulators. An initial ansatz close to perturbation theory is later extended by adding a Fierz complete set of local four-fermion interactions. Flow equations for the gauge coupling, fermion mass and wave function renormalization as well as the four-fermion couplings are derived in detail. Hereby, a helpful observation about how the Wetterich equation determines a Fierz over-completeness of an ansatz is made. The resulting equations are studied with primary interest for a finite number of colours and fermion flavours, but their infinite limits are also considered bridging to the 't Hooft model. The solutions to the flow equations signal the formation of mesonic bound states where a resonance is found which is independent of the dynamics of the gauge coupling. This is in contrast to the four-dimensional theory in addition to the fact that the scale of the breakdown of the perturbative truncation is determined by the microscopic value of the gauge coupling in this super-renormalizable theory. The technical simplifications of the two-dimensional compared to the four-dimensional theory become apparent in this work and open the possibility to resolve the momentum dependence of the four-fermion interactions in new completeness in future projects.