  Motivated by the recent numerical evidence[1] of a short-range resonating
valence bond state in the honeycomb lattice Hubbard model, we consider
Schwinger boson mean field theories of possible spin liquid states on honeycomb
lattice. From general stability considerations the possible spin liquids will
have gapped spinons coupled to Z$_2$ gauge field. We apply the projective
symmetry group(PSG) method to classify possible Z$_2$ spin liquid states within
this formalism on honeycomb lattice. It is found that there are only two
relevant Z$_2$ states, differed by the value of gauge flux, zero or $\pi$, in
the elementary hexagon. The zero-flux state is a promising candidate for the
observed spin liquid and continuous phase transition into commensurate N\'eel
order. We also derive the critical field theory for this transition, which is
the well-studied O(4) invariant theory[2-4], and has an irrelevant coupling
between Higgs and boson fields with cubic power of spatial derivatives as
required by lattice symmetry. This is in sharp contrast to the conventional
theory[5], where such transition generically leads to non-colinear
incommensurate magnetic order. In this scenario the Z$_2$ spin liquid could be
close to a tricritical point. Soft boson modes will exist at seven different
wave vectors. This will show up as low frequency dynamical spin susceptibility
peaks not only at the $\Gamma$ point (the N\'eel order wave vector) but also at
Brillouin zone edge center $M$ points and twelve other points. Some simple
properties of the $\pi$-flux state are studies as well. Symmetry allowed
further neighbor mean field ansatz are derived in Appendix which can be used in
future theoretical works along this direction.
