Self-dual chiral boson: augmented superfield approach

Abstract

We exploit the standard tools and techniques of the augmented version of the Bonora-Tonin superfield formalism to derive the off-shell nilpotent and absolutely anticommuting (anti-)Becchi-Rouet-Stora-Tyutin (BRST) and (anti-)co-BRST symmetry transformations for the BRSTinvariant Lagrangian density of a self-dual bosonic system. In the derivation of the full set of the above symmetry transformations, we invoke the (dual-)horizontality conditions, and (anti-)BRST-and (anti-)co-BRST-invariant restrictions on the superfields that are defined on the (2, 2)-dimensional supermanifold. The latter is parameterized by the bosonic variable x μ (μ = 0, 1) and a pair of Grassmannian variables θ andθ (with θ 2 =θ 2 = 0 and θθ +θθ = 0). The dynamics of this system is such that, instead of the full (2, 2)-dimensional superspace coordinates (x μ , θ,θ), we require only the specific (1, 2)-dimensional super-subspace variables (t, θ,θ) for its description. This is a novel observation in the context of the superfield approach to the BRST formalism. The application of the dual-horizontality condition, in the derivation of a set of proper (anti-)co-BRST symmetries, is also one of the new ingredients of our present endeavor where we have exploited the augmented version of the superfield approach to the BRST formalism.

Gauged Floreanini–Jackiw type chiral boson and its BRST quantization

“…In Ref [10], we find an interesting description towards quantization of that free FJ type chiral boson. In a very resent work [11], we find an application of augmented super field approach to derive the off-shell nilpotent and absolutely anti-commuting (anti-)BRST and (anti-)co-BRST symmetry transformations for the BRST invariant Lagrangian density of a free chiral boson. Another recent important development towards the BFV quantization of the free chiral boson along with study of Hodge decomposition theorem in the context of conserved charges has came in [12] The obvious generalization of free chiral boson is to take into account of the interaction of gauge field with that and this interacting field theoretical model is known as gauged model of chiral boson.…”

(Anti)chiral Superfield Approach to Nilpotent Symmetries: Self-Dual Chiral Bosonic Theory

“…Further, we have found that the geometrical interpretation for the symmetry transformations remains intact in our present method of derivation vis-à-vis the ones where the mathematical strength of the (dual-)horizontality conditions is properly utilized [37]. Thus, both methods of derivation are consistent and, in some cases, complementary to each other (see, e.g., [20,21,33,34]).…”

Christ–Lee Model: Augmented Supervariable Approach

“…The invariance of gauge-fixing term under the (anti-)co-BRST transformations can be captured in the following (anti-)co-BRST invariant restriction [17,28] ⋆d ⋆Z (1)…”

“…For the interacting theories, a more powerful method known as "augmented" version of the superfield approach has been developed where, in addition to the horizontality condition, the gauge-invariant restrictions are also implemented for the derivation of the complete set of proper (anti-)BRST transformations [27][28][29][30]. In our present study, we shall utilize the power and strength of the superfield formalism to derive the off-shell nilpotent and absolutely anticommuting (anti-)BRST as well as (anti-)co-BRST symmetry transformations for the (0+1)-dimensional CL model.…”