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.

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• Dirac fermions
• Quantum spin liquid
• Spinon
• Density matrix renormalization group
• SU(N) symmetries