Anomalous gauge theories with antisymmetric tensor fields

Abstract

We derive a dual theory of the four-dimensional anomalous U(1) gauge theory with a Wess-Zumino (WZ) term and with a Stückelberg type mass term by means of a duality transformation at each of the classical and quantum levels. It is shown that in the dual anomalous U(1) gauge theory, the BF term with a rank-two antisymmetric tensor field plays the roles of the WZ term as well as the mass term of the U(1) gauge field. Similar anomalous U(1) gauge theory with BF term is considered in six-dimensions by introducing a rank-four antisymmetric tensor field. In addition to this theory, we propose a six-dimensional anomalous U(1) gauge theory including an extended BF term with a rank-two antisymmetric tensor field, discussing a difference between the two theories. We also consider a four-dimensional anomalous SU(2)×U(1) gauge theory with BF term and recognize a crucial role of the BF term in cancelling the non-abelian chiral anomaly.

The Stueckelberg Field

“…The idea of inventing new fields in order to uncover or make manifest hidden symmetries has been applied in many contexts. The extension of the Stueckelberg formalism for a massive antisymmetric field (Kalb and Ramond, 1974) has been the subject of intensive research Barcelos-Neto et al, 1996;Deguchi and Kokubo, 2002;Deguchi et al, 1999;Kuzmin and McKeon, 2002;Sawayanagi, 1995;Smailagic and Spallucci, 2001), approaching a clear understanding (Diamantini, 2001). The generalization to p-forms (p = 2 for the Kalb-Ramond field) has met with success (Bizdadea, 1996;Bizdadea et al, 1999;Bizdadea and Saliu, 1998).…”

A universal Lagrangian for massive Yang–Mills theories without residual Higgs bosons

“…Thus, using an equation of motion, L A reduces to L AS or L TA ; the Lagrangians L AS and L TA are classically equivalent. Their equivalence is also established at the quantum level by using the path-integral method [10]. Equations ( 14) and ( 16) give the relation mA µ − ∂ µ ϕ = 1 6 ǫ µνρσ H νρσ , which demonstrates the duality between ϕ and B µν .…”

Dualization between supersymmetric self-dual and topologically massive models coupled to matter in four-dimensional superspace

“…The Maxwell-Kalb-Ramond (MKR) theory is gauge invariant, unitary, and renormalizable when minimally coupled to fermions and represents a massive spin-1 particle [32]. The Kalb-Ramond field appears in several contexts in the literature, in particular we can mention its study within contexts of string theories [38], quantum field theory [39,40], supersymmetry [41], Lorentz symmetry violation [42][43][44][45], black hole solutions [46], cosmology [47,48], and brane words scenarios [49,50].…”