Abelian 2-form gauge theory: superfield formalism

Abstract

Abstract:We derive the off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for all the fields of a free Abelian 2-form gauge theory by exploiting the geometrical superfield approach to BRST formalism. The above four (3 + 1)-dimensional (4D) theory is considered on a (4, 2)-dimensional supermanifold parameterized by the four even spacetime variables x µ (with µ = 0, 1, 2, 3) and a pair of odd Grassmannian variables θ andθ (with θ 2 =θ 2 = 0, θθ +θθ = 0). One of the salient features of our present investigation is that the above nilpotent (anti-)BRST symmetry transformations turn out to be absolutely anticommuting due to the presence of a Curci-Ferrari (CF) type of restriction. The latter condition emerges due to the application of our present superfield formalism. The actual CF condition, as is well-known, is the hallmark of a 4D non-Abelian 1-form gauge theory. We demonstrate that our present 4D Abelian 2-form gauge theory imbibes some of the key signatures of the 4D non-Abelian 1-form gauge theory. We briefly comment on the generalization of our supperfield approach to the case of Abelian 3-form gauge theory in four (3 + 1)-dimensions of spacetime.

Superfield Approach to Nilpotency and Absolute Anticommutativity of Conserved Charges: 2D Non-Abelian 1-Form Gauge Theory

“…Thus, we observe that the nilpotency of the charges ( ) and ( ) is deeply connected with the nilpotency of the (anti-)-co-BRST symmetries (i.e., (8) and (9)) and ( ) = has already been proven in (9). This happens because of the fact that the expressions for ( ) and ( ) are the same as given in (8) for the Lagrangian densities (1).…”

“…In our earlier works [9][10][11][12], we have never been able to capture the nilpotency as well as absolute anticommutativity properties of the (anti-)BRST and (anti-)co-BRST charges. The central objective of our present paper is to achieve this goal in the case of 2D nonAbelian 1-form gauge theory.…”

“…It does not shed any light on the (anti-)BRST symmetries that are associated with the matter fields in a given interacting gauge theory. In a set of papers [9][10][11][12], the above usual superfield formalism has been systematically generalized so as to derive the (anti-)BRST symmetries for the gauge, matter, and (anti)ghost fields 2 Advances in High Energy Physics together. The latter superfield approach [9][10][11][12] has been christened as the augmented version of superfield approach to BRST formalism, where, consistent with the HC, additional restrictions (i.e., gauge invariant conditions) are also invoked.…”

“…In a set of papers [9][10][11][12], the above usual superfield formalism has been systematically generalized so as to derive the (anti-)BRST symmetries for the gauge, matter, and (anti)ghost fields 2 Advances in High Energy Physics together. The latter superfield approach [9][10][11][12] has been christened as the augmented version of superfield approach to BRST formalism, where, consistent with the HC, additional restrictions (i.e., gauge invariant conditions) are also invoked. We shall exploit the latter superfield approach [9][10][11][12] to discuss a few key features of the 2D non-Abelian 1-form gauge theory (without any interaction with matter fields) which have already been discussed within the framework of BRST formalism [13][14][15][16].…”

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

“…Furthermore, the CF-type conditions also play an important role in the derivation of coupled (but equivalent) Lagrangian densities. These CF-type conditions emerge automatically within the framework of superfield formalism [11][12][13]. The emergence of CF-type of condition(s) is one of the characteristic features of a p-form (non-)Abelian gauge theory within the framework of superfield approach to BRST formalism.…”