24,813 research outputs found
BRST cohomology and Hodge decomposition theorem in Abelian gauge theory
We discuss the Becchi-Rouet-Stora-Tyutin (BRST) cohomology and Hodge
decomposition theorem for the two dimensional free U(1) gauge theory. In
addition to the usual BRST charge, we derive a local, conserved and nilpotent
co(dual)-BRST charge under which the gauge-fixing term remains invariant. We
express the Hodge decomposition theorem in terms of these charges and the
Laplacian operator. We take a single photon state in the quantum Hilbert space
and demonstrate the notion of gauge invariance, no-(anti)ghost theorem,
transversality of photon and establish the topological nature of this theory by
exploiting the concepts of BRST cohomology and Hodge decomposition theorem. In
fact, the topological nature of this theory is encoded in the vanishing of the
Laplacian operator when equations of motion are exploited. On the two
dimensional compact manifold, we derive two sets of topological invariants with
respect to the conserved and nilpotent BRST- and co-BRST charges and express
the Lagrangian density of the theory as the sum of terms that are BRST- and
co-BRST invariants. Mathematically, this theory captures together some of the
key features of both Witten- and Schwarz type of topological field theories.Comment: 20 pages, LaTeX, no figures, Title and text have been changed,
Journal reference is given, some references have been adde
Topological aspects in non-Abelian gauge theory
We discuss the BRST cohomology and exhibit a connection between the Hodge
decomposition theorem and the topological properties of a two dimensional free
non-Abelian gauge theory having no interaction with matter fields. The
topological nature of this theory is encoded in the vanishing of the Laplacian
operator when equations of motion are exploited. We obtain two sets of
topological invariants with respect to BRST and co-BRST charges on the two
dimensional manifold and show that the Lagrangian density of the theory can be
expressed as the sum of terms that are BRST- and co-BRST invariants.Comment: (1+11) pages, LaTeX, no figure
Three Brane Action and The Correspondence Between N=4 Yang Mills Theory and Anti De Sitter Space
Recently, a relation between N=4 Super Yang Mills in 3+1 dimensions and
supergravity in an background has been proposed. In this paper we
explore the idea that the correspondence between operators in the Yang Mills
theory and modes of the supergravity theory can be obtained by using the D3
brane action. Specifically, we consider two form gauge fields for this purpose.
The supergravity analysis predicts that the operator which corresponds to this
mode has dimension six. We show that this is indeed the leading operator in the
three brane Dirac-Born-Infeld and Wess-Zumino action which couples to this
mode. It is important in the analysis that the brane action is expanded around
the anti de-Sitter background. Also, the Wess-Zumino term plays a crucial role
in cancelling a lower dimension operator which appears in the the
Dirac-Born-Infeld action.Comment: 12 pages, LaTex, no figures; error in the form of the final dimension
six operator corrected, some references and comments added, main conclusions
unchange
SECOR observations in the Pacific
Geometric adjustment technique for Pacific SECOR observations based on least squares metho
Dual Projection and Selfduality in Three Dimensions
We discuss the notion of duality and selfduality in the context of the dual
projection operation that creates an internal space of potentials. Contrary to
the prevailing algebraic or group theoretical methods, this technique is
applicable to both even and odd dimensions. The role of parity in the kernel of
the Gauss law to determine the dimensional dependence is clarified. We derive
the appropriate invariant actions, discuss the symmetry groups and their proper
generators. In particular, the novel concept of duality symmetry and
selfduality in Maxwell theory in (2+1) dimensions is analysed in details. The
corresponding action is a 3D version of the familiar duality symmetric
electromagnetic theory in 4D. Finally, the duality symmetric actions in the
different dimensions constructed here manifest both the SO(2) and
symmetries, contrary to conventional results.Comment: 20 pages, late
Kaluza-Klein electrically charged black branes in M-theory
We present a class of Kaluza-Klein electrically charged black p-brane
solutions of ten-dimensional, type IIA superstring theory. Uplifting to eleven
dimensions these solutions are studied in the context of M-theory. They can be
interpreted either as a p+1 extended object trapped around the eleventh
dimension along which momentum is flowing or as a boost of the following
backgrounds: the Schwarzschild black (p+1)-brane or the product of the
(10-p)-dimensional Euclidean Schwarzschild manifold with the (p+1)-dimensional
Minkowski spacetime.Comment: 16 pages, uses latex and epsf macro, figures include
Abelian Duality
We show that on three-dimensional Riemannian manifolds without boundaries and
with trivial first real de Rham cohomology group (and in no other dimensions)
scalar field theory and Maxwell theory are equivalent: the ratio of the
partition functions is given by the Ray-Singer torsion of the manifold. On the
level of interaction with external currents, the equivalence persists provided
there is a fixed relation between the charges and the currents.Comment: 11 pages, LaTeX, no figures, a reference added, submitted to Phys.
Rev.
A Note on Marginally Stable Bound States in Type II String Theory
Spectrum of elementary string states in type II string theory contains
ultra-short multiplets that are marginally stable. -duality transformation
converts these states into bound states at threshold of -branes carrying
Ramond-Ramond charges, and wrapped around -cycles of a torus. We propose a
test for the existence of these marginally stable bound states. Using the
recent results of Polchinski and of Witten, we argue that the spectrum of bound
states of -branes is in agreement with the prediction of -duality.Comment: LaTeX file, 6 page
Aspects of BRST Quantization
BRST-methods provide elegant and powerful tools for the construction and
analysis of constrained systems, including models of particles, strings and
fields. These lectures provide an elementary introduction to the ideas,
illustrated with some important physical applications.Comment: Lectures presented at the summerschool `Geometry and Topology in
Physics', Rot a/d/ Rot (Germany), sept. 2001; 75 page
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