Superfield approach to (non-)local symmetries for 1-form Abelian gauge theory

Abstract

Abstract:We exploit the geometrical superfield formalism to derive the local, covariant and continuous Becchi-Rouet-Stora-Tyutin (BRST) symmetry transformations and the non-local, non-covariant and continuous dual-BRST symmetry transformations for the free Abelian one-form gauge theory in four (3+1)-dimensions (4D) of spacetime. Our discussion is carried out in the framework of BRST invariant Lagrangian density for the above 4D theory in the Feynman gauge. The geometrical origin and interpretation for the (dual-)BRST charges (and the transformations they generate) are provided in the language of translations of some superfields along the Grassmannian directions of the six (4 + 2)-dimensional supermanifold parametrized by the four spacetime and two Grassmannian variables. *

Hodge Duality Operation and Its Physical Applications on Supermanifolds

“…(iv) The Hodge duality ⋆ operation for some selected super-forms on a six (4 + 2)-dimensional supermanifold have been defined in our earlier work [42]. However, some ad-hoc assumptions have been made in [42]. No such assumptions have been made in our present Hodge duality ⋆ definitions.…”

“…(2.15)), correspond to such numerical factors present in the definition of ordinary forms on the ordinary spacetime manifold. (iv) The Hodge duality ⋆ operation for some selected super-forms on a six (4 + 2)-dimensional supermanifold have been defined in our earlier work [42]. However, some ad-hoc assumptions have been made in [42].…”

“…All the rest of the steps are exactly the same (see, e.g., equations (2.8)-(2.12)) as discussed in the sub-section 2.1 for the discussion of the 2D Abelian theory on a (2 + 2)-dimensional supermanifold. Finally, the horizontality conditioñ dà (1) = dA (1) leads to the derivation of the nilpotent (anti-)BRST symmetry transformations (3.3) for the 4D free Abelian gauge theory as expressed below in the language of the superfield expansion on the six (4 + 2)-dimensional supermanifold (see, e.g., [42] for details) (cf. (3.3)) for the local fields (A µ , C,C).…”

Nilpotent Symmetries for a Free Relativistic Particle in Augmented Superfield Formalism

“…In a set of papers [15][16][17][18][19], all the three (super)cohomological operators have been exploited to derive the (anti-)BRST symmetries, (anti-)co-BRST symmetries and a bosonic symmetry for the two-dimensional free Abelian gauge theory in the superfield formulation where the generalized versions of the horizontality condition have been exploited. All the above attempts [6][7][8][9][10][11][12][13][14][15][16][17][18][19], however, have not yet been able to shed any light on the nilpotent symmetries that exist for the matter fields of an interacting gauge theory. Thus, the results of the above approaches [6][7][8][9][10][11][12][13][14][15][16][17][18][19] are still partial as far as the derivation of all the symmetry transformations are concerned.…”

“…All the above attempts [6][7][8][9][10][11][12][13][14][15][16][17][18][19], however, have not yet been able to shed any light on the nilpotent symmetries that exist for the matter fields of an interacting gauge theory. Thus, the results of the above approaches [6][7][8][9][10][11][12][13][14][15][16][17][18][19] are still partial as far as the derivation of all the symmetry transformations are concerned.Recently, in a set of papers [20][21][22], the restriction due to the horizontality condition has been augmented with the requirement of the invariance of matter (super)currents on the (super)manifolds † . The latter restriction produces the nilpotent (anti-)BRST symmetry transformations for the matter fields of a given interacting gauge theory.…”