7,483 research outputs found
Fermi Coordinates and Penrose Limits
We propose a formulation of the Penrose plane wave limit in terms of null
Fermi coordinates. This provides a physically intuitive (Fermi coordinates are
direct measures of geodesic distance in space-time) and manifestly covariant
description of the expansion around the plane wave metric in terms of
components of the curvature tensor of the original metric, and generalises the
covariant description of the lowest order Penrose limit metric itself, obtained
in hep-th/0312029. We describe in some detail the construction of null Fermi
coordinates and the corresponding expansion of the metric, and then study
various aspects of the higher order corrections to the Penrose limit. In
particular, we observe that in general the first-order corrected metric is such
that it admits a light-cone gauge description in string theory. We also
establish a formal analogue of the Weyl tensor peeling theorem for the Penrose
limit expansion in any dimension, and we give a simple derivation of the
leading (quadratic) corrections to the Penrose limit of AdS_5 x S^5.Comment: 25 page
Localization and Diagonalization: A review of functional integral techniques for low-dimensional gauge theories and topological field theories
We review localization techniques for functional integrals which have
recently been used to perform calculations in and gain insight into the
structure of certain topological field theories and low-dimensional gauge
theories. These are the functional integral counterparts of the Mathai-Quillen
formalism, the Duistermaat-Heckman theorem, and the Weyl integral formula
respectively. In each case, we first introduce the necessary mathematical
background (Euler classes of vector bundles, equivariant cohomology, topology
of Lie groups), and describe the finite dimensional integration formulae. We
then discuss some applications to path integrals and give an overview of the
relevant literature. The applications we deal with include supersymmetric
quantum mechanics, cohomological field theories, phase space path integrals,
and two-dimensional Yang-Mills theory.Comment: 72 pages (60 A4 pages), LaTeX (to appear in the Journal of
Mathematical Physics Special Issue on Functional Integration (May 1995)
Black holes in Godel universes and pp-waves
We find exact rotating and non-rotating neutral black hole solutions in the
Godel universe of the five dimensional minimal supergravity theory. We also
describe the embedding of this solution in M-theory. After dimensional
reduction and T-duality, we obtain a supergravity solution corresponding to
placing a black string in a pp-wave background.Comment: 9 pages, 1 figur
2D Yang-Mills Theory as a Matrix String Theory
Quantization of two-dimensional Yang-Mills theory on a torus in the gauge
where the field strength is diagonal leads to twisted sectors that are
completely analogous to the ones that originate long string states in Matrix
String Theory. If these sectors are taken into account the partition function
is different from the standard one found in the literature and the invariance
of the theory under modular transformations of the torus appears to hold in a
stronger sense. The twisted sectors are in one-to-one correspondence with the
coverings of the torus without branch points, so they define by themselves a
string theory. A possible duality between this string theory and the
Gross-Taylor string is discussed, and the problems that one encounters in
generalizing this approach to interacting strings are pointed out. This talk is
based on a previous paper by the same authors, but it contains some new results
and a better interpretation of the results already obtained.Comment: 11 pages, LaTeX, 2 figures included with epsf. Talk presented at the
2nd Conference on Quantum aspects of Gauge Theories, Supersymmetry and
Unification, Corfu, Greece, 21-26 September 199
Penrose Limits and Non-local theories
We investigate Penrose limits of two classes of non-local theories, little
string theories and non-commutative gauge theories. Penrose limits of the
near-horizon geometry of NS5-branes help to shed some light on the high energy
spectrum of little string theories. We attempt to understand renormalization
group flow in these theories by considering Penrose limits wherein the null
geodesic also has a radial component. In particular, we demonstrate that it is
possible to construct a pp-wave spacetime which interpolates between the linear
dilaton and the AdS regions for the Type IIA NS5-brane. Similar analysis is
considered for the holographic dual geometry to non-commutative field theories.Comment: 27 pages, LaTeX; v2: added reference
On solvable models of type IIB superstring in NS-NS and R-R plane wave backgrounds
We consider type IIB string in the two plane-wave backgrounds which may be
interpreted as special limits of the AdS_3 x S^3 metric supported by either the
NS-NS or R-R 3-form field. The NS-NS plane-wave string model is equivalent to a
direct generalization of the Nappi-Witten model, with its spectrum being
similar to that of strings in constant magnetic field. The R-R model can be
solved in the light-cone gauge, where the Green-Schwarz action describes 4
massive and 4 massless copies of free bosons and fermions. We find the spectra
of the two string models and study the asymptotic density of states. We also
discuss a more general class of exactly solvable plane-wave models with reduced
supersymmetry which is obtained by adding twists in two spatial 2-planes.Comment: 36 pages, harvmac. v2: discussion of equivalence of the supergravity
parts of the spectra of the NS-NS and R-R models added in sect.5.3; v3: added
remark on periodicity of the NS-NS spectrum; v4: minor correction in sect.6.
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