  We describe a new class of spin liquids with global SU(2) spin rotation
symmetry in spin 1/2 systems on the triangular lattice, which have real
Majorana fermion excitations carrying spin S = 1. The simplest
translationally-invariant mean-field state on the triangular lattice breaks
time-reversal symmetry and is stable to fluctuations. It generically possesses
gapless excitations along 3 Fermi lines in the Brillouin zone. These intersect
at a single point where the excitations scale with a dynamic exponent z = 3. An
external magnetic field has no orbital coupling to the SU(2) spin
rotation-invariant fermion bilinears that can give rise to a transverse thermal
conductivity, thus leading to the absence of a thermal Hall effect. The Zeeman
coupling is found to gap out two-thirds of the z = 3 excitations near the
intersection point and this leads to a suppression of the low temperature
specific heat, the spin susceptibility and the Wilson ratio. We also compute
physical properties in the presence of weak disorder and discuss possible
connections to recent experiments on organic insulators.
