On free 4D Abelian 2-form and anomalous 2D Abelian 1-form gauge theories

Details On free 4D Abelian 2-form and anomalous 2D Abelian 1-form gauge theories On free 4D Abelian 2-form and anomalous 2D Abelian 1-form gauge theories

2009-05-07

arxiv.org/abs/0905.0934v3

Eur.Phys.J.C65:311-329,2010

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX file, 37 pages, version to appear in EPJC

Scientific paper

10.1140/epjc/s10052-009-1205-x

We demonstrate a few striking similarities and some glaring differences between (i) the free four (3 + 1)-dimensional (4D) Abelian 2-form gauge theory, and (ii) the anomalous two (1 + 1)-dimensional (2D) Abelian 1-form gauge theory, within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. We demonstrate that the Lagrangian densities of the above two theories transform in a similar fashion under a set of symmetry transformations even though they are endowed with a drastically different variety of constraint structures. Taking the help of our understanding of the 4D Abelian 2-form gauge theory, we prove that the gauge invariant version of the anomalous 2D Abelian 1-form gauge theory is a new field-theoretic model for the Hodge theory where all the de Rham cohomological operators of differential geometry find their physical realizations in the language of proper symmetry transformations. The corresponding conserved charges obey an algebra that is reminiscent of the algebra of the cohomological operators. We briefly comment on the consistency of the 2D anomalous 1-form gauge theory in the language of restrictions on the harmonic state of the (anti-) BRST and (anti-) co-BRST invariant version of the above 2D theory.

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