Superunitary operator and BRST transformations of a non-Abelian two-form

Abstract

Using superspace unitary operator formalism, we derive various (anti-)BRST symmetry transformations explicitly for the non-Abelian 2-form gauge theories. We introduce a new Lagrangian with a coupling of matter fields not only with 1-from background field but also with a 2-form field. Moreover, the two gauge fields couple mutually as well. A new covariant derivative involving the 2-form gauge field is introduced. We also put forth a conjecture to generalise this idea to any p-form gauge theory.1 BRST is the abbreviation of the names of its founders, viz. Becchi, Rouet, Stora and Tyutin.1-form gauge and corresponding ghost and anti-ghost fields can be derived exploiting the so-called horizontality condition (HC). This condition is basically equating the supercurvature 2-form defined on (D + 2)-dimensional superspace to the ordinary curvature 2-form defined on the D-dimensional Minkowski spacetime. To include interacting systems where the gauge field couples to matter fields, this formalism has been consistently generalised to obtain the (anti-)BRST transformations for the matter fields as well, which is called the augmented superfield formalism [14,15,16,17], where, in addition to the horizontality condition, some gauge-invariant restrictions (GIRs) are also exploited. The mapping of ordinary fields on the Minkowski spacetime to the superfields on the superspace can also be carried out via a superspace unitary operator [9,10,11,18,19], or superunitary operator for short. The superunitary operator upgrades the fields and gauge connections to their superspace-counterparts in the same fashion as the unitary gauge operator maps the fields and gauge connections to their gauge-transformed counterparts. This superunitary operator is determined from the horizontality condition and gauge-invariant restrictions.Our goal in this paper is to deduce the (anti-)BRST transformation for the Kalb-Raymond B-field 2-form, following the superunitary operator approach. For that we consider the interacting theory where the matter fields interact with the 1-form as well as the 2-form gauge field. The two gauge fields, too, interact with each-other through the well known B ∧ F interaction term. Our focus would be to find out the (anti-)BRST symmetry transformations for the various fields and to obtain the corresponding covariant derivatives for both the gauge fields, i.e. for 1-form and 2-form gauge connections.We start with a brief review, in Sec. 2, of 1-form gauge theories, (anti-)BRST transformations and the idea of superfields and superunitary operator. Exploiting the horizontality condition and the gauge-invariant restrictions, the superunitary operator is obtained which upgrades the fields to their superspace-counterparts. The expansion of the superfields in terms of the ordinary fields yields the (anti-)BRST transformations of that field. We have incorporated the matter fields also and both the Abelian and non-Abelian cases are discussed. In Sec. 3, we extend the superunitary operator formalism to 2-form non-Abelian gauge theories...