I will review some problems of the black hole paradigm and explore other possibilities for the final state of stellar collapse other than an evaporating black hole. In particular I will use the so-called transplanckian problem as a guide in this search for a compelling scenario for the evaporation of ultracompact objects.
It is widely known in the
quantum information community that the states that satisfy strong subadditivity
of entropy with equality have the form of quantum Markov chain. Based on a
recent strengthening of strong subadditivity of entropy, I will describe how
such structure can be exploited in the studies of gapped quantum many-body
system. In particular, I will describe a diagrammatic trick to i) give a
quantitative statement about the locality of entanglement spectrum ii)
perturbatively bound changes of topological entanglement entropy under generic
perturbation.
The Rosenbluth Method is a classical kinetic growth Monte
Carlo algorithm for growing a self-avoiding walk by appending steps to its
endpoint.
This algorithm
can be generalised by the implementation of more general
elementary moves (for example, BFACF elementary moves) to realise kinetic
growth algorithms for lattice polygons.
This generalises the counting principle that underlies the Rosenbluth
method and the result is a widely applicable class of algorithms which may be
used for microcanonical sampling in discrete models. In addition to self-avoiding walks, several
applications of kinetic growth and canonical Monte Carlo algorithms will be
presented, including the sampling of trivial words in abstract groups, as well
as knotted lattice polygons and discrete lattice spin systems such as the Potts
model.
This is work was done in collaboration with Andrew
Rechnitzer of the Mathematics Department at the University of British Columbia.
Quantum chaos is the study
of quantum systems whose classical description is chaotic.
How does chaos manifest itself in
the quantum world? In recent years, attempts have been made
to address this question from the perspective of quantum information
theory. It is in this spirit that we study the connection
between quantum chaos and information gain in the
time series of a measurement record used for quantum tomography. The
record is obtained as a sequence of expectation values of a Hermitian operator
evolving under repeated application of the Floquet operator of
the quantum kicked top on a large ensemble of identical systems. We
find an increase in information gain and hence higher fidelities
in the process when the Floquet maps employed increase in chaoticity. We make
predictions for the information gain using random matrix theory
in the fully chaotic regime and show a remarkable agreement between
the two.
Two-dimensional gauge
theories with (0,2) supersymmetry admit a much broader, and more interesting,
class of solutions than their better studied (2,2) counterparts. In this talk,
we will explore some of the possibilities that are offered by this additional
freedom. The moduli spaces we find can be interpreted as the target spaces for
heterotic strings moving in backgrounds with non-trivial H-flux. A remarkable
relationship between (0,2) gauge anomalies and H-flux will emerge.
Fluctuations in the cosmic
microwave background (CMB) contain information which has been pivotal in
establishing the current cosmological model. These data can also be used to
test well-motivated additions to this model, such as
cosmic textures. Textures are a type of topological defect that
can be produced during a cosmological phase transition in the early universe,
and which leave characteristic hot and cold spots in the CMB. We apply Bayesian
methods to carry out an optimal test of the texture hypothesis, using
full-sky data from the Wilkinson Microwave Anisotropy Probe. We conclude that
current data do not warrant augmenting the standard cosmological model
with textures. We rule out at 95% confidence models that predict more than
6 detectable cosmic textures on the full sky.
We expound several principles in an attempt to clarify
the debate over infrared loop corrections to the primordial scalar and tensor
power spectra from inflation. Among other things we note that existing
proposals for nonlinear extensions of the scalar fluctuation field $\zeta$
introduce new ultraviolet divergences which no one understands how to
renormalize. Loop corrections and higher correlators of these putative
observables would also be enhanced by inverse powers of the slow roll parameter
$\epsilon$. We propose an extension which might be better behaved.
We analyze the
implications for Susy theories of a Higgs to di-photon rate enhanced, if
compared to the Standard Model prediction. We show how models predicting a
sizable enhancement have generically an electroweak vacuum that is not
absolutely stable. In particular we discuss the only viable scenario that can
predict sizable new physics effects in the di-photon rate in the framework of
the MSSM: a scenario with light and heavily mixed staus. We conclude with the
phenomenology of this model and with the prospects of probing it at the LHC,
through the direct production of light staus.
Cosmological
birefringence is a postulated rotation of the linear polarization of photons
that arises due to a Chern-Simons coupling of a new scalar field to
electromagnetism. In particular, it appears as a generic feature of simple
quintessence models for Dark Energy, and therefore, should it be detected,
could provide insight into the microphysics of cosmic acceleration. Prior work
has sought this rotation, assuming the rotation angle to be uniform across the
sky, by looking for the parity-violating TB and EB correlations in the CMB
temperature/polarization. However, if the scalar field that gives rise to
cosmological birefringence has spatial fluctuations, then the rotation angle
may vary across the sky. In this talk, I will present the results of the first
CMB-based search for direction-dependent cosmological birefringence, using
WMAP-7 data, and report the constraint on the rotation-angle power spectrum for
all multipoles up to the resolution of the instrument. I will discuss the
implications for a specific models for rotation, and show forecasts for Planck
and future experiments. I will then conclude with a brief discussion of other
exotic physical models, such as chiral gravity, and astrophysical scenarios,
such as inhomogeneous reionization, that can be probed using the same analysis.