Self-dual chiral boson: augmented superfield approach

D. Shukla; T. Bhanja; R. P. Malik

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

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2014) 74: 3025
https://doi.org/10.1140/epjc/s10052-014-3025-x

Regular Article - Theoretical Physics

Self-dual chiral boson: augmented superfield approach

D. Shukla¹, T. Bhanja¹ and R. P. Malik¹^,2^*

¹ Department of Physics, Faculty of Science, Centre of Advanced Studies, Banaras Hindu University, Varanasi, 221 005, U.P., India
² Faculty of Science, DST Centre for Interdisciplinary Mathematical Sciences, Banaras Hindu University, Varanasi, 221 005, U.P., India

^* e-mail: malik@bhu.ac.in

Received: 29 April 2014
Accepted: 6 August 2014
Published online: 16 September 2014

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 BRST-invariant 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 $x^\mu \,(\mu = 0,\, 1)$ and a pair of Grassmannian 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 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.