Exact solution of two-dimensional Poincaré gravity coupled to fermion matter

The two-dimensional model of gravity with zweibeins ${\mathit{e}}^{\mathit{a}}$ and the Lorentz connection one-form ${\mathrm{\omega }}_{\mathit{b}}^{\mathit{a}}$ as independent gravitational variables coupled to 2D massless Dirac matter is considered. It is shown that the classical equations of motion are exactly integrated and the general solution is found in the case of chiral fermions.