Self-dual chiral boson: augmented superfield approach

D Shukla,R P Malik,T Bhanja

doi:10.1140/epjc/s10052-014-3025-x

D Shukla, R P Malik + Show 1 more

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https://doi.org/10.1140/epjc/s10052-014-3025-x

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Abstract

We exploit the standard tools and techniques of the augmented version of Bonora-Tonin (BT) superfield formalism to derive the off-shell nilpotent and absolutely anticommuting (anti-)BRST and (anti-)co-BRST symmetry transformations for the Becchi-Rouet-Stora-Tyutin (BRST) invariant Lagrangian density of a self-dual bosonic system. In the derivation of the full set of the above transformations, we invoke the (dual-)horizontality conditions, (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^\mu\,(\mu = 0,\, 1) and a pair of Grassmanian variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0 and \theta\bar\theta + \bar\theta\theta = 0). The dynamics of this system is such that, instead of the full (2, 2) dimensional superspace coordinates (x^\mu, \theta, \bar\theta), we require only the specific (1, 2)-dimensional super-subspace variables (t, \theta, \bar\theta) for its description. This is a novel observation in the context of superfield approach to 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 superfield formalism which is geometrically very intuitive.

Highlights

The above superfield approach to the BRST formalism is one of the geometrically intuitive methods that shed light on the abstract mathematical properties associated with the properBRST symmetries in the language of geometrical objects on the supermanifold
To obtain the off-shell nilpotent and absolutely anticommutingBRST symmetry transformations for φ(t) and v(t) variables, we have to exploit the key ideas of the augmented version of the BT-superfield formalism [16,17,18,19] where we demand that all theBRST-invariant quantities should remain independent of the “soul” coordinates (i.e., θ and θ) when they are generalized to the supermanifold
We have provided the geometrical basis for the above nilpotent symmetries in the language of the nilpotent (i.e. ∂θ2 = 0, ∂θ2 ̄ = 0) translational generators (∂θ, ∂θ) along the Grassmannian directions (θ, θ) of our chosen (2, 2)-dimensional supermanifold [parameterized by Z M =] on which our present 2D ordinary field theory has been generalized

Summary

Introduction

The above superfield approach to the BRST formalism is one of the geometrically intuitive methods that shed light on the abstract mathematical properties associated with the proper (anti-)BRST symmetries in the language of geometrical objects on the supermanifold. To derive the (anti-)BRST symmetry transformations (6) within the framework of the augmented superfield formalism, first of all, we generalize the basic variables of the 2D theory onto the (2, 2)-dimensional supermanifold as follows: φ(x) −→ ̃ (x, θ, θ), v(x) −→ V (x, θ, θ), C(x) −→ F(x, θ, θ), C (x) −→ F (x, θ, θ), λ(x) −→ λ (x, θ, θ), (17)

Results

Conclusion