Spontaneous Lorentz Symmetry Breaking by Anti-Symmetric Tensor Field

We study the spontaneous Lorentz symmetry breaking in a field theoretical model in (2+1)-dimension, inspired by string theory. This model is a gauge theory of an anti-symmetric tensor field and a vector field (photon). The Nambu-Goldstone (NG) boson for the spontaneous Lorentz symmetry breaking is identified with the unphysical massless photon in the covariant quantization. We also discuss an analogue of the equivalence theorem between the amplitudes for emission or absorption of the physical massive anti-symmetric tensor field and those of the unphysical massless photon. The low-energy effective action of the NG-boson is also discussed.