11 research outputs found
Abelian 2-form gauge theory: superfield formalism
We derive the off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and
anti-BRST symmetry transformations for {\it all} the fields of a free Abelian
2-form gauge theory by exploiting the geometrical superfield approach to BRST
formalism. The above four (3 + 1)-dimensional (4D) theory is considered on a
(4, 2)-dimensional supermanifold parameterized by the four even spacetime
variables x^\mu (with \mu = 0, 1, 2, 3) and a pair of odd Grassmannian
variables \theta and \bar\theta (with \theta^2 = \bar\theta^2 = 0, \theta
\bar\theta + \bar\theta \theta = 0). One of the salient features of our present
investigation is that the above nilpotent (anti-)BRST symmetry transformations
turn out to be absolutely anticommuting due to the presence of a Curci-Ferrari
(CF) type of restriction. The latter condition emerges due to the application
of our present superfield formalism. The actual CF condition, as is well-known,
is the hallmark of a 4D non-Abelian 1-form gauge theory. We demonstrate that
our present 4D Abelian 2-form gauge theory imbibes some of the key signatures
of the 4D non-Abelian 1-form gauge theory. We briefly comment on the
generalization of our supperfield approach to the case of Abelian 3-form gauge
theory in four (3 + 1)-dimensions of spacetime.Comment: LaTeX file, 23 pages, journal versio
Expansions of algebras and superalgebras and some applications
After reviewing the three well-known methods to obtain Lie algebras and
superalgebras from given ones, namely, contractions, deformations and
extensions, we describe a fourth method recently introduced, the expansion of
Lie (super)algebras. Expanded (super)algebras have, in general, larger
dimensions than the original algebra, but also include the Inonu-Wigner and
generalized IW contractions as a particular case. As an example of a physical
application of expansions, we discuss the relation between the possible
underlying gauge symmetry of eleven-dimensional supergravity and the
superalgebra osp(1|32).Comment: Invited lecture delivered at the 'Deformations and Contractions in
Mathematics and Physics Workshop', 15-21 January 2006, Mathematisches
Forschungsinstitut Oberwolfach, German
On free 4D Abelian 2-form and anomalous 2D Abelian 1-form gauge theories
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.Comment: LaTeX file, 37 pages, version to appear in EPJ