Expectation values, Lorentz invariance, and $\text{CPT}$ in the open bosonic string

Abstract

The issue of spontaneous breaking of Lorentz and $\text{CPT}$ 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 $\text{CPT}$-preserving solution previously suggested in the literature is confirmed through level 12 in the action. A family of Lorentz-breaking, $\text{CPT}$-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 $\text{CPT}$ are discussed. The analysis at this level involves the analytical form of over 20,000 terms in the static potential.