345 research outputs found
Quantum evolution across singularities
Attempts to consider evolution across space-time singularities often lead to
quantum systems with time-dependent Hamiltonians developing an isolated
singularity as a function of time. Examples include matrix theory in certain
singular time-dependent backgounds and free quantum fields on the
two-dimensional compactified Milne universe. Due to the presence of the
singularities in the time dependence, the conventional quantum-mechanical
evolution is not well-defined for such systems. We propose a natural way,
mathematically analogous to renormalization in conventional quantum field
theory, to construct unitary quantum evolution across the singularity. We carry
out this procedure explicitly for free fields on the compactified Milne
universe and compare our results with the matching conditions considered in
earlier work (which were based on the covering Minkowski space).Comment: revised with an emphasis on local counterterm subtraction rather than
analyticity; version to be submitted for publicatio
Light-like Big Bang singularities in string and matrix theories
Important open questions in cosmology require a better understanding of the
Big Bang singularity. In string and matrix theories, light-like analogues of
cosmological singularities (singular plane wave backgrounds) turn out to be
particularly tractable. We give a status report on the current understanding of
such light-like Big Bang models, presenting both solved and open problems.Comment: 20 pages, invited review for Class. Quant. Grav; v3: section 2.3
shortened, discussion on DLCQ added in section 3.1, published versio
Orbifold boundary states from Cardy's condition
Boundary states for D-branes at orbifold fixed points are constructed in
close analogy with Cardy's derivation of consistent boundary states in RCFT.
Comments are made on the interpretation of the various coefficients in the
explicit expressions, and the relation between fractional branes and wrapped
branes is investigated for orbifolds. The boundary states
are generalised to theories with discrete torsion and a new check is performed
on the relation between discrete torsion phases and projective representations.Comment: LaTeX2e, 50 pages, 5 figures. V3: final version to appear on JHEP
(part of a section moved to an appendix, titles of some references added, one
sentence in the introduction expanded
p-branes on the waves
We present a large family of simple, explicit ten-dimensional supergravity
solutions describing extended extremal supersymmetric Ramond-Ramond p-branes
embedded into time-dependent dilaton-gravity plane waves of an arbitrary
(isotropic) profile, with the brane world-volume aligned parallel to the
propagation direction of the wave. Generalizations to the non-extremal case are
not analyzed explicitly, but can be pursued as indicated.Comment: 11 pages; v.2 minor notation changes, minor typos corrected
(published version
Quantum evolution across singularities: the case of geometrical resolutions
We continue the study of time-dependent Hamiltonians with an isolated
singularity in their time dependence, describing propagation on singular
space-times. In previous work, two of us have proposed a "minimal subtraction"
prescription for the simplest class of such systems, involving Hamiltonians
with only one singular term. On the other hand, Hamiltonians corresponding to
geometrical resolutions of space-time tend to involve multiple operator
structures (multiple types of dependence on the canonical variables) in an
essential way.
We consider some of the general properties of such (near-)singular
Hamiltonian systems, and further specialize to the case of a free scalar field
on a two-parameter generalization of the null-brane space-time. We find that
the singular limit of free scalar field evolution exists for a discrete subset
of the possible values of the two parameters. The coordinates we introduce
reveal a peculiar reflection property of scalar field propagation on the
generalized (as well as the original) null-brane. We further present a simple
family of pp-wave geometries whose singular limit is a light-like hyperplane
(discontinuously) reflecting the positions of particles as they pass through
it.Comment: 25 pages, 1 figur
Holography and Cosmological Singularities
Certain null singularities in ten dimensional supergravity have natural
holographic duals in terms of Matrix Theory and generalizations of the AdS/CFT
correspondence. In many situations the holographic duals appear to be well
defined in regions where the supergravity develops singularities. We describe
some recent progress in this area.Comment: Anomaly equation corrected. References adde
D-Brane Potentials from Multi-Trace Deformations in AdS/CFT
It is known that certain AdS boundary conditions allow smooth initial data to
evolve into a big crunch. To study this type of cosmological singularity, one
can use the dual quantum field theory, where the non-standard boundary
conditions are reflected by the presence of a multi-trace potential unbounded
below. For specific AdS_4 and AdS_5 models, we provide a D-brane (or M-brane)
interpretation of the unbounded potential. Using probe brane computations, we
show that the AdS boundary conditions of interest cause spherical branes to be
pushed to the boundary of AdS in finite time, and that the corresponding
potential agrees with the multi-trace deformation of the dual field theory.
Systems with expanding spherical D3-branes are related to big crunch
supergravity solutions by a phenomenon similar to geometric transition.Comment: 26 pages, 3 figures, v4: a few typos fixed
Can free strings propagate across plane wave singularities?
We study free string propagation in families of plane wave geometries
developing strong scale-invariant singularities in certain limits. We relate
the singular limit of the evolution for all excited string modes to that of the
center-of-mass motion (the latter existing for discrete values of the overall
plane wave profile normalization). Requiring that the entire excitation energy
of the string should be finite turns out to be quite restrictive and
essentially excludes consistent propagation across the singularity, unless
dimensionful scales are introduced at the singular locus (in an otherwise
scale-invariant space-time).Comment: 24 pages; v.2: published version, minor clarifications adde
Shock Waves and Cosmological Matrix Models
We find the shock wave solutions in a class of cosmological backgrounds with
a null singularity, each of these backgrounds admits a matrix description. A
shock wave solution breaks all supersymmetry meanwhile indicates that the
interaction between two static D0-branes cancel, thus provides basic evidence
for the matrix description. The probe action of a D0-brane in the background of
another suggests that the usual perturbative expansion of matrix model breaks
down.Comment: 10 pages, harvmav, v2: some comments on instability added, v3:
version to appear in JHE
- …