  We present a new auxiliary field representation for the four-fermi term of
the gauge-fixed Green-Schwarz superstring action which describes fluctuations
around the null-cusp background in $AdS_5\times S^5$. We sketch the main
features of the fermionic operator spectrum, identifying the region of
parameter space where the sign ambiguity is absent. Measurements for the
observables in the setup here described are presented and discussed in a
forthcoming publication.
