Expectation Values, Lorentz Invariance, and CPT in the Open Bosonic String

TL;DR

This paper investigates spontaneous Lorentz and CPT symmetry breaking in open bosonic string theory using a level truncation approach, confirming some solutions and discovering new symmetry-breaking solutions through detailed potential analysis.

Contribution

It provides the first systematic level-truncation analysis of Lorentz and CPT symmetry breaking in open bosonic strings, confirming known solutions and identifying new symmetry-breaking solutions.

Findings

Confirmed Lorentz- and CPT-preserving solutions at level 12.

Discovered a family of Lorentz-breaking, CPT-preserving solutions up to level 18.

Identified solutions that spontaneously break both Lorentz invariance and CPT, involving over 20,000 terms in the potential.

Abstract

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.