  By combining the density matrix renormalization group (DMRG) method with
Gutzwiller projected wave functions, we study the SU(4) symmetric spin-orbital
model on the honeycomb lattice. We find that the ground states can be well
described by a Gutzwiller projected $\pi$-flux state with Dirac-type gapless
excitations at one quarter filling. Although these Dirac points are gapped by
emergent gauge fluxes on finite cylinders, they govern the critical behavior in
the thermodynamic limit. By inserting a $\theta=\pi$ spin flux to twist the
boundary condition, we can shift the gapless sector to the ground state, which
provides compelling evidence for the presence of a gapless Dirac spin-orbital
liquid.
