Discrete Duality Symmetry in a 3D Field-Theoretic Model

Abstract: We demonstrate the discrete duality symmetry between the Abelian 1-form and 2-form basic gauge fields in the context of a three (2 + 1)-dimensional (3D) combined system of the field-theoretic model for the combined system of the free Abelian 1-from and 2-form gauge theories within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism where the classical gauge-fixed Lagrangian density of this theory is generalized to its quantum counterpart as the BRST and co-BRST invariant Lagrangian density. We show clearly the existence of the off-shell nilpotent (co-)BRST symmetry transformations and establish their intimate connection through a set of underlying discrete duality symmetry transformations in our BRST-quantized theory. We provide the mathematical basis for the existence of the discrete duality symmetry transformations in our theory through the Hodge duality operator (that is defined on the 3D flat Minkowskian spacetime manifold). We briefly mention a bosonic symmetry transformation which is constructed from the anticommutator of the above off-shell nilpotent (co-)BRST symmetry transformations. We lay emphasis on the algebraic structures of the existing continuous and discrete duality symmetry transformations in our theory (where they are treated as operators).