752 research outputs found
A Class of Cosmological Matrix Models
We discuss a class of matrix models describing cosmology with a light-like
singularity, generalizing the model proposed by Craps et al. in hep-th/0506180.Comment: 12 pages, harvmac, v2: final version published in Phys. Lett.
Exactly Solvable Model of Superstring in Plane-wave Background with Linear Null Dilaton
In this paper, we study an exactly solvable model of IIB superstring in a
time-dependent plane-wave backgound with a constant self-dual Ramond-Ramond
5-form field strength and a linear dilaton in the light-like direction. This
background keeps sixteen supersymmetries. In the light-cone gauge, the action
is described by the two-dimensional free bosons and fermions with
time-dependent masses. The model could be canonically quantized and its
Hamiltonian is time-dependent with vanishing zero point energy. The spectrum of
the excitations is symmetric between the bosonic and fermionic sector. The
string mode creation turns out to be very small.Comment: 35 pages, Latex; Acknowledgement added; Published versio
Homogeneous Plane Waves
Motivated by the search for potentially exactly solvable time-dependent
string backgrounds, we determine all homogeneous plane wave (HPW) metrics in
any dimension and find one family of HPWs with geodesically complete metrics
and another with metrics containing null singularities. The former generalises
both the Cahen-Wallach (constant ) metrics to time-dependent HPWs,
, and the Ozsvath-Sch\"ucking anti-Mach metric to arbitrary
dimensions. The latter is a generalisation of the known homogeneous metrics
with to a more complicated time-dependence. We display these
metrics in various coordinate systems, show how to embed them into string
theory, and determine the isometry algebra of a general HPW and the associated
conserved charges. We review the Lewis-Riesenfeld theory of invariants of
time-dependent harmonic oscillators and show how it can be deduced from the
geometry of plane waves. We advocate the use of the invariant associated with
the extra (timelike) isometry of HPWs for lightcone quantisation, and
illustrate the procedure in some examples.Comment: 48 pages, LaTeX2e, v2: additional references and cosmetic correction
Matrix Model in a Class of Time Dependent Supersymmetric Backgrounds
We discuss the matrix model in a class of 11D time dependent supersymmetric
backgrounds as obtained in hep-th/0508191 . We construct the matrix model
action through the matrix regularization of the membrane action in the
background. We show that the action is exact to all order of fermionic
coordinates. Furthermore We discuss the fuzzy sphere solutions in this
background.Comment: 16 pages, 4 figures; references added, modifications of some comments
in introduction, version to appear in PL
Plane waves with weak singularities
We study a class of time dependent solutions of the vacuum Einstein equations
which are plane waves with weak null singularities. This singularity is weak in
the sense that though the tidal forces diverge at the singularity, the rate of
divergence is such that the distortion suffered by a freely falling observer
remains finite. Among such weak singular plane waves there is a sub-class which
do not exhibit large back reaction in the presence of test scalar probes.
String propagation in these backgrounds is smooth and there is a natural way to
continue the metric beyond the singularity. This continued metric admits string
propagation without the string becoming infinitely excited. We construct a one
parameter family of smooth metrics which are at a finite distance in the space
of metrics from the extended metric and a well defined operator in the string
sigma model which resolves the singularity.Comment: 22 pages, Added references and clarifying comment
On the instability of 3d null singularities
String propagation on a three-dimensional Lorentzian string orbifold with a
null singularity has been studied by Horowitz and Steif, and more recently by
Liu, Moore and Seiberg. We analyze the target space as a classical
gravitational background. The singularity becomes spacelike when an arbitrarily
small amount of matter is thrown at the singularity. This can be seen directly
by studying the null singularity as a limit of the M=0, J=0 BTZ black hole
metric.Comment: 9 pages, uses harvmac.tex. v2: minor wording changes in introduction,
fixed reference typo, new reference
4-Dimensional BF Theory as a Topological Quantum Field Theory
Starting from a Lie group G whose Lie algebra is equipped with an invariant
nondegenerate symmetric bilinear form, we show that 4-dimensional BF theory
with cosmological term gives rise to a TQFT satisfying a generalization of
Atiyah's axioms to manifolds equipped with principal G-bundle. The case G =
GL(4,R) is especially interesting because every 4-manifold is then naturally
equipped with a principal G-bundle, namely its frame bundle. In this case, the
partition function of a compact oriented 4-manifold is the exponential of its
signature, and the resulting TQFT is isomorphic to that constructed by Crane
and Yetter using a state sum model, or by Broda using a surgery presentation of
4-manifolds.Comment: 15 pages in LaTe
A Space-Time Orbifold: A Toy Model for a Cosmological Singularity
We explore bosonic strings and Type II superstrings in the simplest time
dependent backgrounds, namely orbifolds of Minkowski space by time reversal and
some spatial reflections. We show that there are no negative norm physical
excitations. However, the contributions of negative norm virtual states to
quantum loops do not cancel, showing that a ghost-free gauge cannot be chosen.
The spectrum includes a twisted sector, with strings confined to a ``conical''
singularity which is localized in time. Since these localized strings are not
visible to asymptotic observers, interesting issues arise regarding unitarity
of the S-matrix for scattering of propagating states. The partition function of
our model is modular invariant, and for the superstring, the zero momentum
dilaton tadpole vanishes. Many of the issues we study will be generic to
time-dependent cosmological backgrounds with singularities localized in time,
and we derive some general lessons about quantizing strings on such spaces.Comment: 21 pages, 2 figure
Precursors, black holes, and a locality bound
We revisit the problem of precursors in the AdS/CFT correspondence.
Identification of the precursors is expected to improve our understanding of
the tension between holography and bulk locality and of the resolution of the
black hole information paradox. Previous arguments that the precursors are
large, undecorated Wilson loops are found to be flawed. We argue that the role
of precursors should become evident when one saturates a certain locality
bound. The spacetime uncertainty principle is a direct consequence of this
bound.Comment: 26 pages, 8 figs; reference added, minor clarification in sec. 2;
incorrect draft mistakenly used in version
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