Can the Nambu-Goldstone Boson Live on the Light Front?

Abstract

We show that the Nambu-Goldstone (NG) boson restricted on the light front (LF) can only exist if we regularize the theory by introducing the explicit symmetry breaking NG-boson mass ${m}_{\ensuremath{\pi}}$. The NG-boson zero mode, when integrated over the LF, must have a singular behavior $\ensuremath{\sim}1/{m}_{\ensuremath{\pi}}^{2}$ in the symmetric limit of ${m}_{\ensuremath{\pi}}^{2}\ensuremath{\rightarrow}0$. In the discretized LF quantization this peculiarity is clarified in terms of the zero-mode constraints in the linear $\ensuremath{\sigma}$ model. The LF charge annihilates the vacuum, while it is not conserved in the symmetric limit in the NG phase.