Fermions in 2d Lorentzian quantum gravity

We implement Wilson fermions on 2d Lorentzian triangulation and determine the spectrum of the Dirac-Wilson operator. We compare it to the spectrum of the corresponding operator in the Euclidean background. We use fermionic particle to probe the fractal properties of Lorentzian gravity coupled to c = 1/2 and c 4 matter. We numerically determine the scaling exponent of the mass gap M similar to N-1/dH to be d(H) 2.11(5), and d(H)= 1.77(3) for c = 1/2 and c = 4, respectively.