Our group studied 1+1 dim QCD in light cone coordinates 15 years ago; you should look for papers from "F. Lenz" and "M. Thies" - unfortunately not in arxiv.
The main difference in light cone coordinates is the following
p = (p0, p1, p2, ...) => (p+, p-, p2, ...)
The dispersion relation for massive particles reads:
p+ = (... + m²) / 2p-
where ... means the perpendicular components.
Due to this dispersion relation for the light cone energy p+ the Dirac sea becomes trivial; there is a unique solution for p+ for given light cone momentum p- ; that means that a sea-particle cannot be excited w/o violation of the light cone momentum. Therefore a "mixing" of quarks and anti-quarks is forbidden = the vacuum structure is trivial.
Nevertheless you can find non-vanishing condensates, but in a different formalism.
The light cone gauge for a gauge field A then means
A- = 0
It is comparable to the axial gauge, that means
- one polarization is eliminated completely
- a "Coulomb potential" arises due to invertion of the Gauss constraint
Usually one derives a Hamiltonian framework (one has to check for Poincare covariance)
In some sense the light cone frame is related to the infinite momentum frame.
As far as I know the light cone approach is not widely used in QCD; the trivial vacuum structure seems to be a benefit when one starts with the calculations, but there are other difficulties like non-dynamical fermionic degrees of freedom (in 1+1 dim. you can see that one component of the spinor is non-dynamical as there is no light cone time derivative) and the non-local light cone energy operator.
I have no idea how this relates to string theory.