Random magnetic field and the Dirac Fermi surface

We study a single two-dimensional Dirac fermion at finite density, subject to quenched random magnetic field. At low energies and sufficiently weak disorder, the theory maps onto an infinite collection of 1D chiral fermions (associated each point on Fermi surface) coupled by vector potential. This low-energy exhibits exactly solvable fixed line, along which we directly compute various disorder-averaged observables without need for usual replica, supersymmetry, or Keldysh techniques. find longitudinal dc conductivity in collisionless $\ensuremath{\hbar}\ensuremath{\omega}/{k}_{B}T\ensuremath{\rightarrow}\ensuremath{\infty}$ limit be nonuniversal vary continuously line.