Framework Of Superfield Formalism Research Articles

The Batalin–Vilkovisky formalism description of self-dual Chern–Simons gauge theory coupled to matter fields in superspace

We construct the extended BRST and anti-BRST transformation by considering a shift symmetry both in Abelian and non-Abelian Chern–Simons theories coupled to scalar fields using the approach of Batalin–Vilkovisky quantization. The extended BRST invariant Lagrangian density is able to be addressed in the framework of superfield formalism with one fermionic coordinate. In the case of extended BRST–anti-BRST symmetry, it is shown that the Batalin–Vilkovisky action of the theory can be expressed in a covariant form with two fermionic coordinates in the superspace.

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

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 which 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.

NILPOTENT SYMMETRY INVARIANCE IN THE SUPERFIELD FORMULATION: THE (NON-)ABELIAN 1-FORM GAUGE THEORIES

We capture the off-shell as well as the on-shell nilpotent Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian densities of the four (3+1)-dimensional (4D) (non-)Abelian 1-form gauge theories within the framework of the superfield formalism. In particular, we provide the geometrical interpretations for (i) the above nilpotent symmetry invariance, and (ii) the above Lagrangian densities, in the language of the specific quantities defined in the domain of the above superfield formalism. Some of the subtle points, connected with the 4D (non-)Abelian 1-form gauge theories, are clarified within the framework of the above superfield formalism where the 4D ordinary gauge theories are considered on the (4, 2)-dimensional supermanifold parametrized by the four space–time coordinates xμ (with μ = 0, 1, 2, 3) and a pair of Grassmannian variables θ and [Formula: see text]. One of the key results of our present investigation is a great deal of simplification in the geometrical understanding of the nilpotent (anti-)BRST symmetry invariance.

Superfield approach to symmetries for matter fields in Abelian gauge theories

The derivation of the nilpotent Becchi–Rouet–Stora–Tyutin (BRST)- and anti-BRST symmetries for the matter fields, present in any arbitrary interacting gauge theory, has been a long-standing problem in the framework of superfield approach to the BRST formalism. These nilpotent (anti-)BRST symmetries for the Dirac fields are derived in the superfield formulation for the interacting Abelian gauge theory in four (3 + 1)-dimensions (4D) of spacetime. The same type of symmetries are deduced for the 4D complex scalar fields having a gauge-invariant interaction with the U(1) gauge field. The above interacting theories are considered on a six (4 + 2)-dimensional supermanifold parametrized by four even spacetime coordinates and a couple of odd elements of the Grassmann algebra. The invariance of the conserved matter (super)currents and the horizontality condition on the (super)manifolds play very important roles in the above derivations. The geometrical origin and interpretation for all the above off-shell nilpotent symmetries are provided in the framework of superfield formalism.

Nilpotent symmetries for QED in superfield formalism

In the framework of superfield approach, we derive the local, covariant, continuous and nilpotent (anti-)BRST and (anti-)co-BRST symmetry transformations on the U(1) gauge field (Aμ) and the (anti-)ghost fields ((C̄)C) of the Lagrangian density of the two (1+1)-dimensional QED by exploiting the (dual-)horizontality conditions defined on the four (2+2)-dimensional supermanifold. The long-standing problem of the derivation of the above symmetry transformations for the matter (Dirac) fields (ψ̄,ψ) in the framework of superfield formulation is resolved by a new set of restrictions on the (2+2)-dimensional supermanifold. These new physically interesting restrictions on the supermanifold owe their origin to the invariance of conserved currents of the theory. The geometrical interpretation for all the above transformations is provided in the framework of superfield formalism.

Topological aspects of Abelian gauge theory in superfield formulation

We discuss some aspects of the topological features of a non-interacting two (1+1)-dimensional Abelian gauge theory in the framework of superfield formalism. This theory is described by a BRST invariant Lagrangian density in the Feynman gauge. We express the local and continuous symmetries, Lagrangian density, topological invariants and symmetric energy momentum tensor of this theory in the language of superfields by exploiting the nilpotent (anti-)BRST- and (anti-)co-BRST symmetries. In particular, the Lagrangian density and symmetric energy momentum tensor of this topological theory turn out to be the sum of terms that geometrically correspond to the translations of some local superfields along the Grassmannian directions of the four (2+2)-dimensional supermanifold. In this interpretation, the (anti-)BRST- and (anti-)co-BRST symmetries, that emerge after the imposition of the (dual) horizontality conditions, play a very important role.

Superfield approach to BRST cohomology

In the framework of superfield formalism, we discuss some aspects of the cohomological features of a two (1+1)-dimensional free Abelian gauge theory described by a Becchi-Rouet-Stora-Tyutin (BRST) invariant Lagrangian density. We demonstrate that the conserved and nilpotent (anti-)BRST- and (anti-)co-BRST charges are the generators of translations along the Grassmannian directions of the four (2+2)-dimensional supermanifold. A bosonic symmetry is shown to be generated by a Noether conserved charge that generates a translation along a bosonic direction of the supermanifold which turns out to be equivalent to a couple of successive translations along the two different and independent Grassmannian directions of the same supermanifold. Algebraically, these charges are found to be analogous to the de Rham cohomology operators of differential geometry.

SUPERFIELD APPROACH TO A NOVEL SYMMETRY FOR NON-ABELIAN GAUGE THEORY

In the framework of superfield formalism, we demonstrate the existence of a new local, covariant, continuous and nilpotent (dual-BRST) symmetry for the BRST invariant Lagrangian density of a self-interacting two (1+1)-dimensional (2D) non-Abelian gauge theory (having no interaction with matter fields). The local and nilpotent Noether conserved charges corresponding to the above continuous symmetries find their geometrical interpretation as the translation generators along the odd (Grassmannian) directions of the four (2+2)-dimensional compact supermanifold.

New symmetries for Abelian gauge theory in superfield formulation

We show the existence of some new local, covariant and continuous symmetries for the BRST invariant Lagrangian density of a free two(1+1)-dimensional (2D) Abelian U (1) gauge theory in the framework of superfield formalism. The Noether conserved charges corresponding to the above local continuous symmetries find their geometrical origin as the translation generators along the odd (Grassmannian) and even (bosonic) directions of the four(2+2)-dimensional compact supermanifold. Some new discrete symmetries are shown to exist in the superfield formulation. The logical origin for the existence of BRST and co-BRST symmetries is shown to be encoded in the Hodge decomposed versions (of the 2D fermionic vector fields) that are consistent with the discrete symmetries of the theory.