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

TL;DR

This paper investigates spontaneous Lorentz symmetry breaking in (2+1) dimensions, deriving the effective action for Nambu-Goldstone bosons using coset construction, and elucidating the symmetry breaking pattern from SO(2,1) to SO(1,1).

Contribution

It introduces a novel application of coset construction to derive the low-energy effective action for symmetry breaking involving an antisymmetric tensor in (2+1) dimensions.

Findings

Derived the Goldstone covariant derivative.

Obtained the covariant gauge field.

Formulated the low-energy effective action.

Abstract

One kind of spontaneous (2+1)-dimensional Lorentz symmetry breaking is discussed. The symmetry breaking pattern is $SO(2,1)\rightarrow SO(1,1)$. 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.