Born–Infeld–Chern–Simons theory: Hamiltonian embedding, duality and bosonization

Abstract

In this paper we study in detail the equivalence of the recently introduced Born–Infeld self-dual model to the Abelian Born–Infeld–Chern–Simons model in 2+1 dimensions. We first apply the improved Batalin, Fradkin and Tyutin scheme, to embed the Born–Infeld self-dual model to a gauge system and show that the embedded model is equivalent to Abelian Born–Infeld–Chern–Simons theory. Next, using Buscher's duality procedure, we demonstrate this equivalence in a covariant Lagrangian formulation and also derive the mapping between the n-point correlators of the (dual) field strength in Born–Infeld–Chern–Simons theory and of basic field in Born–Infeld self-dual model. Using this equivalence, the bosonization of a massive Dirac theory with a non-polynomial Thirring type current–current coupling, to leading order in (inverse) fermion mass is also discussed. We also rederive it using a master Lagrangian. Finally, the operator equivalence between the fermionic current and (dual) field strength of Born–Infeld–Chern–Simons theory is deduced at the level of correlators and using this the current–current commutators are obtained.