Absolutely anticommuting (anti-)BRST symmetry transformations for topologically massive Abelian gauge theory

Abstract

We demonstrate the existence of the nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the four (3 + 1)-dimensional (4D) topologically massive Abelian U(1) gauge theory that is described by the coupled Lagrangian densities (which incorporate the celebrated (B ∧ F ) term). The absolute anticommutativity of the (anti-) BRST symmetry transformations is ensured by the existence of a Curci-Ferrari type restriction that emerges from the superfield formalism as well as from the equations of motion that are derived from the above coupled Lagrangian densities. We show the invariance of the action from the point of view of the symmetry considerations as well as superfield formulation. We discuss, furthermore, the topological term within the framework of superfield formalism and provide the geometrical meaning of its invariance under the (anti-) BRST symmetry transformations.

Superfield approach to nilpotent symmetries in 3D Jackiw–Pi model of massive non-Abelian theory

“…However, these models suffer from the problems, connected with renormalizability, consistency and unitarity. We have studied these models [5,6,7,8,9,10], within the framework of superfield and Becchi-Rouet-Stora-Tyutin (BRST) formalisms, in the hope that we would be able to propose a model that would be free of the drawbacks of the earlier models [1,2,3,4]. However, it remains still an open problem to construct a 4D consistent, unitary and renormalizable non-Abelian 2-form gauge theory (where the 1-form and 2-form non-Abelian gauge fields are incorporated together).…”

Augmented superfield approach to gauge-invariant massive 2-form theory

“…With the help of superfield formalism, we have derived the off-shell nilpotent as well as absolutely anticommuting (anti-) BRST transformations and also shown that the topological (B ∧ F) term remains unaffected by the presence of the Grassmannian variables when we generalize it on the (4, 2)-dimensional supermanifold [49,50]. In the non-Abelian case, we have found some novel observations.…”

$$(3+1)$$ ( 3 + 1 ) -Dimensional topologically massive 2-form gauge theory: geometrical superfield approach

“…This implies that the topological term remains invariant modulo a total spacetime derivative term under the operations of BRST and/or anti-BRST transformations. Consequently, the superLagrangian densities (48) and (49) remain invariant (up to a total spacetime derivative) under the action of Grassmannian derivatives due to the nilpotency (i.e. ∂ 2 θ = 0, ∂ 2 θ = 0) and anticommutativity (i.e.…”

“…The phenomenological aspects of this model have been discussed in [47] which shed light on the various kind of physical processes that are allowed by the standard model of particle physics. We have also studied the 4D (non-)Abelian topologically massive theory within the framework of BRST formalism [48,49]. In earlier work [10], the 4D non-Abelian topologically massive gauge theory has been studied in the context of superfield formalism where the "scalar" and "vector" gauge symmetries have been treated separately.…”