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

TL;DR

This paper develops a superfield approach to derive nilpotent BRST and co-BRST symmetries for a 2D self-dual chiral bosonic theory, emphasizing symmetry restrictions on (anti-)chiral superfields without using horizontality conditions.

Contribution

It introduces a novel augmented (anti-)chiral superfield formalism to derive nilpotent symmetries, highlighting the absolute anticommutativity property as a new result.

Findings

Derived nilpotent BRST and co-BRST transformations using symmetry restrictions.

Established the absolute anticommutativity property in the superfield formalism.

Analyzed invariance and properties of the Lagrangian density within the framework.

Abstract

We exploit the beauty and strength of the symmetry invariant restrictions on the (anti-)chiral superfields to derive the Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST and (anti-)co-BRST symmetry transformations in the case of a two (1+1)-dimensional (2D) self-dual chiral bosonic field theory within the framework of augmented (anti-)chiral superfield formalism. Our 2D ordinary theory is generalized onto a (2, 2)-dimensional supermanifold which is parameterized by the superspace variable Z^M = (x^\mu, \theta, \bar\theta) where x^\mu (with \mu = 0, 1) are the ordinary 2D bosonic coordinates and (\theta,\, \bar\theta) are a pair of Grassmannian variables with their standard relationships: \theta^2 = {\bar\theta}^2 =0, \theta\,\bar\theta + \bar\theta\theta = 0. We impose the (anti-)BRST and (anti-)co-BRST invariant restrictions on the (anti-)chiral superfields (defined on the (anti-)chiral (2, 1)-dimensional super-submanifolds of the above general (2, 2)-dimensional supermanifold) to derive the above nilpotent symmetries. We do not exploit the mathematical strength of the (dual-)horizontality conditions anywhere in our present investigation. We also discuss the properties of nilpotency, absolute anticommutativity and (anti-)BRST and (anti-)co-BRST symmetry invariance of the Lagrangian density within the framework of our augmented (anti-)chiral superfield formalism. Our observation of the absolute anticommutativity property is a completely novel result in view of the fact that we have considered only the (anti-)chiral superfields in our present endeavor.