Spontaneous Breaking of (2+1)-dimensional Lorentz Symmetry by an antisymmetric tensor

One kind of spontaneous (2+1)-dimensional Lorentz symmetry breaking is discussed. The symmetry breaking pattern is $SO(2,1)\to SO(1,1)$. Using the coset construction formalism, we derive the Goldstone covariant derivative and the associated covariant gauge field. Finally, the two-derivative low-energy effective action of the Nambu-Goldstone bosons is obtained.