55 research outputs found
Generator Matrix Elements For II
Basis states and generator matrix elements are given for the generic
representation of in an basis.Comment: Latex, 17 pages, one figure using epsf published in J. Phys. A: Math.
Gen 28 (1995) 2581-258
On character generators for simple Lie algebras
We study character generating functions (character generators) of simple Lie
algebras. The expression due to Patera and Sharp, derived from the Weyl
character formula, is first reviewed. A new general formula is then found. It
makes clear the distinct roles of ``outside'' and ``inside'' elements of the
integrity basis, and helps determine their quadratic incompatibilities. We
review, analyze and extend the results obtained by Gaskell using the Demazure
character formulas. We find that the fundamental generalized-poset graphs
underlying the character generators can be deduced from such calculations.
These graphs, introduced by Baclawski and Towber, can be simplified for the
purposes of constructing the character generator. The generating functions can
be written easily using the simplified versions, and associated Demazure
expressions. The rank-two algebras are treated in detail, but we believe our
results are indicative of those for general simple Lie algebras.Comment: 50 pages, 11 figure
Hawking Radiation and Ultraviolet Regulators
Polchinski has argued that the prediction of Hawking radiation must be
independent of the details of unknown high-energy physics because the
calculation may be performed using `nice slices', for which the adiabatic
theorem may be used. If this is so, then any calculation using a manifestly
covariant --- and so slice-independent --- ultraviolet regularization must
reproduce the standard Hawking result. We investigate the dependence of the
Hawking radiation on such a short-distance regulator by calculating it using a
Pauli--Villars regularization scheme. We find that the regulator scale,
, only contributes to the Hawking flux by an amount that is
exponentially small in the large variable {\Lambda}/{T_\ssh} \gg 1, where
T_\ssh is the Hawking temperature; in agreement with Polchinski's arguments.
We also solve a technical puzzle concerning the relation between the
short-distance singularities of the propagator and the Hawking effect.Comment: Tex, 11 pages, no figures, new references adde
Hermitian D-brane solutions
A low-energy background field solution describing D-membrane configurations
is constructed which is distinguished by the appearance of a Hermitian metric
on the internal space. This metric is composed of a number of independent
harmonic functions on the transverse space. Thus this construction generalizes
the usual harmonic superposition rule. The BPS bound of these solutions is
shown to be saturated indicating that they are supersymmetric. By means of
T-duality, we construct more solutions of the IIA and IIB theories.Comment: 14 pages, Latex, no figure
Type IIB Matrix Theory at Two Loops
The IKKT matrix model was proposed to be a non-perturbative formulation of
type IIB superstring theory. One of its important consistency criteria is that
the leading one-loop effective interaction between a cluster of type
IIB D-objects should not receive any corrections from higher loop effects for
it to describe accurately the type IIB supergravity results. In analogy with
the BFSS matrix model {\it versus} the eleven-dimensional supergravity example,
we show in this work that the one-loop effective potential in the IKKT matrix
model is also not renormalized at the two-loop order.Comment: 19 pages, Latex, corrected some typos and 1 figure adde
More on Four-Dimensional Extremal Black Holes
We consider an embedding of the extremal four-dimensional
Reissner-Nordstr\"om black hole into type string theory. The equivalent
type configuration, in the D-brane weak-coupling picture, is a bound
state of D1- and D5-branes threaded by fundamental type strings. The
bound state involves also a NSNS solitonic 5-brane, mimicking the role of the
Kaluza-Klein magnetic monopole. The statistical entropy derived by counting the
degeneracy of the BPS-saturated excitations of this bound state agrees
perfectly with the (semiclassical) Bekenstein-Hawking formula.Comment: 19 pages, using Latex, no figure
The Trans-Planckian Problem of Inflationary Cosmology
In most current models of inflation based on a weakly self-coupled scalar
matter field minimally coupled to gravity, the period of inflation lasts so
long that, at the beginning of the inflationary period, the physical
wavelengths of comoving scales which correspond to the present large-scale
structure of the Universe were smaller than the Planck length. Thus, the usual
computations of the spectrum of fluctuations in these models involve
extrapolating low energy physics (both in the matter and gravitational sector)
into regions where this physics is not applicable. In this paper we demonstrate
that the usual predictions of inflation for the spectrum of cosmological
fluctuations do indeed depend on the hidden assumptions about super-Planck
scale physics. We introduce a class of modified dispersion relations to mimic
possible effects of super-Planck scale physics, and show that in some cases
important deviations from the usual predictions of inflation are obtained. Some
implications of this result for the unification of fundamental physics and
early Universe cosmology are discussed.Comment: 16 pages, 2 figures. One important correction in the Corley/Jacobson
case with b_m>0 and some misprints corrected. Version published in PR
Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory
This article is meant as a summary and introduction to the ideas of effective
field theory as applied to gravitational systems.
Contents:
1. Introduction
2. Effective Field Theories
3. Low-Energy Quantum Gravity
4. Explicit Quantum Calculations
5. ConclusionsComment: 56 pages, 2 figures, JHEP style, Invited review to appear in Living
Reviews of Relativit
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