Exact Solution of 2D Poincare Gravity Coupled to Fermion Matter
  The 2D model of gravity with zweibeins $e^{a}$ and the Lorentz connection one-form $\omega^{a}_{\ b}$ as independent gravitational variables coupled to 2d massless Dirac matter is considered. It is shown that the classical equations of motion are exactly integrated in the case of chiral fermions. 
S.N.Solodukhin