Abelian 2-form gauge theory: special features

Abstract

It is shown that the four (3 + 1)-dimensional (4D) free Abelian 2-form gauge theory provides an example of (i) a class of field theoretical models for the Hodge theory, and (ii) a possible candidate for the quasi-topological field theory (q-TFT). Despite many striking similarities with some of the key topological features of the two (1 + 1)-dimensional (2D) free Abelian (and self-interacting non-Abelian) gauge theories, it turns out that the 4D free Abelian 2-form gauge theory is not an exact TFT. To corroborate this conclusion, some of the key issues are discussed. In particular, it is shown that the (anti-)BRST and (anti-)co-BRST invariant quantities of the 4D 2-form Abelian gauge theory obey the recursion relations that are reminiscent of the exact TFTs but the Lagrangian density of this theory is not found to be able to be expressed as the sum of (anti-)BRST and (anti-)co-BRST exact quantities as is the case with the topological 2D free Abelian (and self-interacting non-Abelian) gauge theories. *

Gauge Transformations, BRST Cohomology and Wigner's Little Group

“…At the next step, it is the nilpotent (co-)BRST (or (dual-)gauge) symmetry transformations that dictate the reduction process of the degrees of freedom of e µν (k). At this stage, (i) we demonstrate the connection between the T (2) subgroup of the Wigner's little group and the (dual-)gauge (or (co-)BRST) symmetry transformation group when they operate on the doubly reduced polarization tensor e µν (k), and (ii) we comment on the quasi-topological nature [15] of the 4D 2-form Abelian gauge theory in the framework of an extended BRST formalism. Ultimately, in the language of the BRST cohomology w.r.t.…”

“…In a recent paper [15], the above cohomological properties and the quasi-topological nature of the 4D free Abelian 2-form gauge theory have been discussed by exploiting the (anti-)BRST and (anti-)co-BRST symmetries, their corresponding generators, their ensuing algebraic structure and the HDT in the QHSS. A quite different but very interesting aspect of the above discussion is connected with the geometrical interpretations [16][17][18][19][20][21] for all the conserved charges (Q (a)b , Q (a)d , Q w ) and their two-to-one mappings with the cohomological operators (d, δ, ∆) in the framework of superfield formulation [22][23][24][25][26].…”

Augmented superfield approach to gauge-invariant massive 2-form theory

“…Furthermore, within the framework of BRST formalism, the free Abelian 2-form gauge theory in (3 + 1) dimensions of spacetime provides a field-theoretic model for the Hodge theory where all the de Rham cohomological operators (d, δ, ) and Hodge duality ( * ) operation of differential geometry find their physical realizations in the language of the continuous symmetries and discrete symmetry, respectively [46,47]. In addition, it has also been shown that the free Abelian 2-form gauge theory, within the framework of BRST formalism, provides a new kind of quasi-topological field theory (q-TFT), which captures some features of Witten type TFT and a few aspects of Schwarz type TFT [48].…”

Nilpotent Symmetries for a Free Relativistic Particle in Augmented Superfield Formalism

“…In a set of papers [15][16][17][18][19], all the three (super)cohomological operators have been exploited to derive the (anti-)BRST symmetries, (anti-)co-BRST symmetries and a bosonic symmetry for the two-dimensional free Abelian gauge theory in the superfield formulation where the generalized versions of the horizontality condition have been exploited. All the above attempts [6][7][8][9][10][11][12][13][14][15][16][17][18][19], however, have not yet been able to shed any light on the nilpotent symmetries that exist for the matter fields of an interacting gauge theory. Thus, the results of the above approaches [6][7][8][9][10][11][12][13][14][15][16][17][18][19] are still partial as far as the derivation of all the symmetry transformations are concerned.…”

“…All the above attempts [6][7][8][9][10][11][12][13][14][15][16][17][18][19], however, have not yet been able to shed any light on the nilpotent symmetries that exist for the matter fields of an interacting gauge theory. Thus, the results of the above approaches [6][7][8][9][10][11][12][13][14][15][16][17][18][19] are still partial as far as the derivation of all the symmetry transformations are concerned.Recently, in a set of papers [20][21][22], the restriction due to the horizontality condition has been augmented with the requirement of the invariance of matter (super)currents on the (super)manifolds † . The latter restriction produces the nilpotent (anti-)BRST symmetry transformations for the matter fields of a given interacting gauge theory.…”