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 breaking NG-boson mass $m_{\pi }$. The NG-boson zero mode, when integrated over the LF, must have a singular behavior $\sim 1/m_{\pi }^2$ in the symmetric limit of $m_{\pi }^2\to 0$. In the discretized LF quantization this peculiarity is clarified in terms of the zero-mode constraints in the linear $\sigma$ model. The LF charge annihilates the vacuum, while it is not conserved in the symmetric limit in the NG phase.

11pages, Latex file