  The issue of spontaneous breaking of Lorentz and CPT invariance is studied in
the open bosonic string using a truncation scheme to saturate the string-field
action at successively higher levels. We find strong evidence for the existence
of extrema of the action with nonzero expectation values for certain fields.
The Lorentz- and CPT-preserving solution previously suggested in the literature
is confirmed through level 12 in the action. A family of Lorentz-breaking,
CPT-preserving solutions of the equations of motion is found to persist and
converge through level 18 in the action. Two sequences of solutions
spontaneously breaking both Lorentz invariance and CPT are discussed. The
analysis at this level involves the analytical form of over 20,000 terms in the
static potential.
