4 research outputs found
Coordinate-invariant Path Integral Methods in Conformal Field Theory
We present a coordinate-invariant approach, based on a Pauli-Villars measure,
to the definition of the path integral in two-dimensional conformal field
theory. We discuss some advantages of this approach compared to the operator
formalism and alternative path integral approaches. We show that our path
integral measure is invariant under conformal transformations and field
reparametrizations, in contrast to the measure used in the Fujikawa
calculation, and we show the agreement, despite different origins, of the
conformal anomaly in the two approaches. The natural energy-momentum in the
Pauli-Villars approach is a true coordinate-invariant tensor quantity, and we
discuss its nontrivial relationship to the corresponding non-tensor object
arising in the operator formalism, thus providing a novel explanation within a
path integral context for the anomalous Ward identities of the latter. We
provide a direct calculation of the nontrivial contact terms arising in
expectation values of certain energy-momentum products, and we use these to
perform a simple consistency check confirming the validity of the change of
variables formula for the path integral. Finally, we review the relationship
between the conformal anomaly and the energy-momentum two-point functions in
our formalism.Comment: Corrected minor typos. To appear in International Journal of Modern
Physics
Weyl-Conformally-Invariant Lightlike p-Brane Theories: New Aspects in Black Hole Physics and Kaluza-Klein Dynamics
We introduce and study in some detail the properties of a novel class of
Weyl-conformally invariant p-brane theories which describe intrinsically
lightlike branes for any odd world-volume dimension. Their dynamics
significantly differs from that of the ordinary (conformally non-invariant)
Nambu-Goto p-branes. We present explicit solutions of the Weyl-invariant
lightlike brane- (WILL-brane) equations of motion in various gravitational
models of physical relevance exhibiting various new phenomena. In D=4 the
WILL-membrane serves as a material and charged source for gravity and
electromagnetism in the coupled Einstein-Maxwell-WILL-membrane system; it
automatically positions itself on (``straddles'') the common event horizon of
the corresponding matching black hole solutions, thus providing an explicit
dynamical realization of the membrane paradigm in black hole physics. In
product spaces of interest in Kaluza-Klein theories the WILL-brane wraps
non-trivially around the compact (internal)dimensions and still describes
massless mode dynamics in the non-compact (space-time) dimensions. Due to
nontrivial variable size of the internal compact dimensions we find new types
of physically interesting solutions describing massless brane modes trapped on
bounded planar circular orbits with non-trivial angular momentum, and with
linear dependence between energy and angular momentum.Comment: 28 pages, published versio