1,258 research outputs found
DLCQ and Plane Wave Matrix Big Bang Models
We study the generalisations of the Craps-Sethi-Verlinde matrix big bang
model to curved, in particular plane wave, space-times, beginning with a
careful discussion of the DLCQ procedure. Singular homogeneous plane waves are
ideal toy-models of realistic space-time singularities since they have been
shown to arise universally as their Penrose limits, and we emphasise the role
played by the symmetries of these plane waves in implementing the flat space
Seiberg-Sen DLCQ prescription for these curved backgrounds. We then analyse
various aspects of the resulting matrix string Yang-Mills theories, such as the
relation between strong coupling space-time singularities and world-sheet
tachyonic mass terms. In order to have concrete examples at hand, in an
appendix we determine and analyse the IIA singular homogeneous plane wave -
null dilaton backgrounds.Comment: 29 pages, v2: reference added + minor cosmetic correction
Blackfolds, Plane Waves and Minimal Surfaces
Minimal surfaces in Euclidean space provide examples of possible non-compact
horizon geometries and topologies in asymptotically flat space-time. On the
other hand, the existence of limiting surfaces in the space-time provides a
simple mechanism for making these configurations compact. Limiting surfaces
appear naturally in a given space-time by making minimal surfaces rotate but
they are also inherent to plane wave or de Sitter space-times in which case
minimal surfaces can be static and compact. We use the blackfold approach in
order to scan for possible black hole horizon geometries and topologies in
asymptotically flat, plane wave and de Sitter space-times. In the process we
uncover several new configurations, such as black helicoids and catenoids, some
of which have an asymptotically flat counterpart. In particular, we find that
the ultraspinning regime of singly-spinning Myers-Perry black holes, described
in terms of the simplest minimal surface (the plane), can be obtained as a
limit of a black helicoid, suggesting that these two families of black holes
are connected. We also show that minimal surfaces embedded in spheres rather
than Euclidean space can be used to construct static compact horizons in
asymptotically de Sitter space-times.Comment: v2: 67pp, 7figures, typos fixed, matches published versio
Chern-Simons Theory on Seifert 3-Manifolds
We study Chern-Simons theory on 3-manifolds M that are circle-bundles over
2-dimensional orbifolds S by the method of Abelianisation. This method, which
completely sidesteps the issue of having to integrate over the moduli space of
non-Abelian flat connections, reduces the complete partition function of the
non-Abelian theory on M to a 2-dimensional Abelian theory on the orbifold S
which is easily evaluated.Comment: 27 page
New Geometries for Black Hole Horizons
We construct several classes of worldvolume effective actions for black holes
by integrating out spatial sections of the worldvolume geometry of
asymptotically flat black branes. This provides a generalisation of the
blackfold approach for higher-dimensional black holes and yields a map between
different effective theories, which we exploit by obtaining new hydrodynamic
and elastic transport coefficients via simple integrations. Using Euclidean
minimal surfaces in order to decouple the fluid dynamics on different sections
of the worldvolume, we obtain local effective theories for ultraspinning
Myers-Perry branes and helicoidal black branes, described in terms of a
stress-energy tensor, particle currents and non-trivial boost vectors. We then
study in detail and present novel compact and non-compact geometries for black
hole horizons in higher-dimensional asymptotically flat space-time. These
include doubly-spinning black rings, black helicoids and helicoidal -branes
as well as helicoidal black rings and helicoidal black tori in .Comment: v2: 37pp, 5figures, typos fixed, matches published versio
Equivariant Kaehler Geometry and Localization in the G/G Model
We analyze in detail the equivariant supersymmetry of the model. In
spite of the fact that this supersymmetry does not model the infinitesimal
action of the group of gauge transformations, localization can be established
by standard arguments. The theory localizes onto reducible connections and a
careful evaluation of the fixed point contributions leads to an alternative
derivation of the Verlinde formula for the WZW model. We show that the
supersymmetry of the model can be regarded as an infinite dimensional
realization of Bismut's theory of equivariant Bott-Chern currents on K\"ahler
manifolds, thus providing a convenient cohomological setting for understanding
the Verlinde formula. We also show that the supersymmetry is related to a
non-linear generalization (q-deformation) of the ordinary moment map of
symplectic geometry in which a representation of the Lie algebra of a group
is replaced by a representation of its group algebra with commutator . In the large limit it reduces to the ordinary moment map of
two-dimensional gauge theories.Comment: LaTex file, 40 A4 pages, IC/94/108 and ENSLAPP-L-469/9
On Subleading Contributions to the AdS/CFT Trace Anomaly
In the context of the AdS/CFT correspondence, we perform a direct computation
in AdS_5 supergravity of the trace anomaly of a d=4, N=2 SCFT. We find
agreement with the field theory result up to next to leading order in the 1/N
expansion. In particular, the order N gravitational contribution to the anomaly
is obtained from a Riemann tensor squared term in the 7-brane effective action
deduced from heterotic - type I duality. We also discuss, in the AdS/CFT
context, the order N corrections to the trace anomaly in d=4, N=4 SCFTs
involving SO or Sp gauge groups.Comment: 25 pages, LaTeX, v2: references adde
The Universality of Penrose Limits near Space-Time Singularities
We prove that Penrose limits of metrics with arbitrary singularities of
power-law type show a universal leading u^{-2}-behaviour near the singularity
provided that the dominant energy condition is satisfied and not saturated. For
generic power-law singularities of this type the oscillator frequencies of the
resulting homogeneous singular plane wave turn out to lie in a range which is
known to allow for an analytic extension of string modes through the
singularity. The discussion is phrased in terms of the recently obtained
covariant characterisation of the Penrose limit; the relation with null
geodesic deviation is explained in detail.Comment: 36 pages, LaTeX2e, 4 figure
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