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We argue for the existence of a liquid ground state in a class of squarelattice models of orbitally degenerate insulators. Starting with the SU(4)symmetric Kugel-Khomskii model, we utilize a Majorana Fermion representation ofspin-orbital operators to access novel phases. Variational wavefunctions ofcandidate liquid phases are thus obtained, whose properties are evaluated usingVariational Monte Carlo. These states are disordered, and are found to haveexcellent energetics and ground state overlap ($>40%$) when compared with exactdiagonalization on 16 site clusters. We conclude that these are spin-orbitalliquid ground states with emergent nodal fermions and Z$_2$ gauge fields.Connections to spin 3/2 cold atom systems and properties in the absence ofSU(4) symmetry are briefly discussed.

A Z$_2$ spin-orbital liquid state in the square lattice Kugel-Khomskii model