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 ZM=xμ,θ,θ¯, where xμ (with μ=0,1) are the ordinary 2D bosonic coordinates and (θ,θ¯) are a pair of Grassmannian variables with their standard relationships: θ2=θ¯2=0, θθ¯+θ¯θ=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 supersubmanifolds 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.
Highlights
The model of the 2D self-dual chiral bosonic field theory has found applications in different areas of research in theoretical physics, for example, models ofstrings, W-gravities, quantum Hall effect, and 2D statistical systems
The usual superfield approach [18,19,20,21,22,23,24] to Becchi-RouetStora-Tyutin (BRST) formalism takes into account the mathematical strength and beauty of the horizontality condition (HC) to obtain the off-shell nilpotent and absolutely anticommutingBRST symmetry transformations for the gauge and associatedghost fields of a given p-form (p = 1, 2, 3, . . .) gauge theory
We conclude that the nilpotency and absolute anticommutativity properties of theco-BRST charges (and the continuous symmetries s(a)d they generate) are intimately connected with such properties associated with the translational generators (∂θ, ∂θ) along the Grassmannian directions of the (2, 1)-dimensional chiral and antichiral supersubmanifolds of the general (2, 2)dimensional supermanifold
Summary
The model of the 2D self-dual chiral bosonic field theory has found applications in different areas of research in theoretical physics, for example, models of (super)strings, W-gravities, quantum Hall effect, and 2D statistical systems (see, e.g., [1,2,3,4,5,6,7,8,9,10,11,12] for details). This has been systematically generalized so as to derive the proper (anti-)BRST symmetry transformations (s(a)b) for the matter, gauge and (anti-)ghost fields together for a given interacting p-form gauge theory (see, e.g., [25,26,27,28]) The latter superfield formalism exploits the additional restrictions (e.g., gauge invariant restrictions) which are found to be consistent with the celebrated HC. We apply the augmented version of the (anti)chiral superfield formalism to the model of 2D self-dual chiral bosonic field theory where we exploit the theoretical power and potential of the symmetry invariant restrictions on the (anti)chiral superfields to derive the proper (anti-)BRST and (anti-)co-BRST symmetry transformations.
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