Exact critical exponents for two-dimensional dense polymers

Using conformal invariance and Coulomb gas results, the author gives the exact value in two dimensions of the eta exponent of L dense polymers, attached by their extremities: eta L =(L 2 -4)/8. The value in two dimensions of the gamma exponent of a dense branched polymer of fixed topology with n L L-leg vertices, L>or=1 is then deduced to be gamma = Sigma L>or=1 n L (2-L)(L+18)/32. These values correspond to a conformally invariant theory with central charge C=-2.