9,772 research outputs found
On the Hagedorn Behaviour of Singular Scale-Invariant Plane Waves
As a step towards understanding the properties of string theory in
time-dependent and singular spacetimes, we study the divergence of density
operators for string ensembles in singular scale-invariant plane waves, i.e.
those plane waves that arise as the Penrose limits of generic power-law
spacetime singularities. We show that the scale invariance implies that the
Hagedorn behaviour of bosonic and supersymmetric strings in these backgrounds,
even with the inclusion of RR or NS fields, is the same as that of strings in
flat space. This is in marked contrast to the behaviour of strings in the BFHP
plane wave which exhibit quantitatively and qualitatively different
thermodynamic properties.Comment: 15 pages, LaTeX2e, v2: JHEP3.cls, one reference adde
Penrose Limits and Spacetime Singularities
We give a covariant characterisation of the Penrose plane wave limit: the
plane wave profile matrix is the restriction of the null geodesic
deviation matrix (curvature tensor) of the original spacetime metric to the
null geodesic, evaluated in a comoving frame. We also consider the Penrose
limits of spacetime singularities and show that for a large class of black
hole, cosmological and null singularities (of Szekeres-Iyer ``power-law
type''), including those of the FRW and Schwarzschild metrics, the result is a
singular homogeneous plane wave with profile , the scale
invariance of the latter reflecting the power-law behaviour of the
singularities.Comment: 9 pages, LaTeX2e; v2: additional references and cosmetic correction
Symmetries and Observables for BF-theories in Superspace
The supersymmetric version of a topological quantum field theory describing
flat connections, the super BF-theory, is studied in the superspace formalism.
A set of observables related to topological invariants is derived from the
curvature of the superspace. Analogously to the non-supersymmetric versions,
the theory exhibits a vector-like supersymmetry. The role of the vector
supersymmetry and an additional new symmetry of the action in the construction
of observables is explained.Comment: 11 pages, LaTe
Scalar Field Probes of Power-Law Space-Time Singularities
We analyse the effective potential of the scalar wave equation near generic
space-time singularities of power-law type (Szekeres-Iyer metrics) and show
that the effective potential exhibits a universal and scale invariant leading
x^{-2} inverse square behaviour in the ``tortoise coordinate'' x provided that
the metrics satisfy the strict Dominant Energy Condition (DEC). This result
parallels that obtained in hep-th/0403252 for probes consisting of families of
massless particles (null geodesic deviation, a.k.a. the Penrose Limit). The
detailed properties of the scalar wave operator depend sensitively on the
numerical coefficient of the x^{-2}-term, and as one application we show that
timelike singularities satisfying the DEC are quantum mechanically singular in
the sense of the Horowitz-Marolf (essential self-adjointness) criterion. We
also comment on some related issues like the near-singularity behaviour of the
scalar fields permitted by the Friedrichs extension.Comment: v2: 21 pages, JHEP3.cls, one reference adde
The Refractive Index of Curved Spacetime II: QED, Penrose Limits and Black Holes
This work considers the way that quantum loop effects modify the propagation
of light in curved space. The calculation of the refractive index for scalar
QED is reviewed and then extended for the first time to QED with spinor
particles in the loop. It is shown how, in both cases, the low frequency phase
velocity can be greater than c, as found originally by Drummond and Hathrell,
but causality is respected in the sense that retarded Green functions vanish
outside the lightcone. A "phenomenology" of the refractive index is then
presented for black holes, FRW universes and gravitational waves. In some
cases, some of the polarization states propagate with a refractive index having
a negative imaginary part indicating a potential breakdown of the optical
theorem in curved space and possible instabilities.Comment: 62 pages, 14 figures, some signs corrected in formulae and graph
An analytic Approach to Turaev's Shadow Invariant
In the present paper we extend the "torus gauge fixing approach" by Blau and
Thompson (Nucl. Phys. B408(1):345--390, 1993) for Chern-Simons models with base
manifolds M of the form M= \Sigma x S^1 in a suitable way. We arrive at a
heuristic path integral formula for the Wilson loop observables associated to
general links in M. We then show that the right-hand side of this formula can
be evaluated explicitly in a non-perturbative way and that this evaluation
naturally leads to the face models in terms of which Turaev's shadow invariant
is defined.Comment: 44 pages, 2 figures. Changes have been made in Sec. 2.3, Sec 2.4,
Sec. 3.4, and Sec. 3.5. Appendix C is ne
Conformal boundary and geodesics for and the plane wave: Their approach in the Penrose limit
Projecting on a suitable subset of coordinates, a picture is constructed in
which the conformal boundary of and that of the plane wave
resulting in the Penrose limit are located at the same line. In a second line
of arguments all and plane wave geodesics are constructed in
their integrated form. Performing the Penrose limit, the approach of null
geodesics reaching the conformal boundary of to that of the
plane wave is studied in detail. At each point these null geodesics of
form a cone which degenerates in the limit.Comment: some statements refined, chapter 5 rewritten to make it more precise,
some typos correcte
Goedel, Penrose, anti-Mach: extra supersymmetries of time-dependent plane waves
We prove that M-theory plane waves with extra supersymmetries are necessarily
homogeneous (but possibly time-dependent), and we show by explicit construction
that such time-dependent plane waves can admit extra supersymmetries. To that
end we study the Penrose limits of Goedel-like metrics, show that the Penrose
limit of the M-theory Goedel metric (with 20 supercharges) is generically a
time-dependent homogeneous plane wave of the anti-Mach type, and display the
four extra Killings spinors in that case. We conclude with some general remarks
on the Killing spinor equations for homogeneous plane waves.Comment: 20 pages, LaTeX2
Topological Aspects of Gauge Fixing Yang-Mills Theory on S4
For an space-time manifold global aspects of gauge-fixing are
investigated using the relation to Topological Quantum Field Theory on the
gauge group. The partition function of this TQFT is shown to compute the
regularized Euler character of a suitably defined space of gauge
transformations. Topological properties of the space of solutions to a
covariant gauge conditon on the orbit of a particular instanton are found using
the isometry group of the base manifold. We obtain that the Euler
character of this space differs from that of an orbit in the topologically
trivial sector. This result implies that an orbit with Pontryagin number
\k=\pm1 in covariant gauges on contributes to physical correlation
functions with a different multiplicity factor due to the Gribov copies, than
an orbit in the trivial \k=0 sector. Similar topological arguments show that
there is no contribution from the topologically trivial sector to physical
correlation functions in gauges defined by a nondegenerate background
connection. We discuss possible physical implications of the global gauge
dependence of Yang-Mills theory.Comment: 13 pages, uuencoded and compressed LaTeX file, no figure
Solvable models of strings in homogeneous plane wave backgrounds
We solve closed string theory in all regular homogeneous plane-wave
backgrounds with homogeneous NS three-form field strength and a dilaton. The
parameters of the model are constant symmetric and anti-symmetric matrices
k_{ij} and f_{ij} associated with the metric, and a constant anti-symmetric
matrix h_{ij} associated with the NS field strength. In the light-cone gauge
the rotation parameters f_{ij} have a natural interpretation as a constant
magnetic field. This is a generalisation of the standard Landau problem with
oscillator energies now being non-trivial functions of the parameters f_{ij}
and k_{ij}. We develop a general procedure for solving linear but non-diagonal
equations for string coordinates, and determine the corresponding oscillator
frequencies, the light-cone Hamiltonian and level matching condition. We
investigate the resulting string spectrum in detail in the four-dimensional
case and compare the results with previously studied examples. Throughout we
will find that the presence of the rotation parameter f_{ij} can lead to
certain unusual and unexpected features of the string spectrum like new
massless states at non-zero string levels, stabilisation of otherwise unstable
(tachyonic) modes, and discrete but not positive definite string oscillator
spectra.Comment: 48 pages, LaTeX2e, v2: additional reference and cosmetic correction
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