154 research outputs found
Symmetry-breaking and zero-one laws
We offer further evidence that discreteness of the sort inherent in a causal set cannot, in and of itself, serve to break Poincaré invariance. In particular we prove that a Poisson sprinkling of Minkowski spacetime cannot endow spacetime with a distinguished spatial or temporal orientation, or with a distinguished lattice of spacetime points, or with a distinguished lattice of timelike directions (corresponding respectively to breakings of reflection-invariance, translation-invariance, and Lorentz invariance). Along the way we provide a proof from first principles of the zero-one law on which our new arguments are based
A Distinguished Vacuum State for a Quantum Field in a Curved Spacetime: Formalism, Features, and Cosmology
We define a distinguished "ground state" or "vacuum" for a free scalar
quantum field in a globally hyperbolic region of an arbitrarily curved
spacetime. Our prescription is motivated by the recent construction of a
quantum field theory on a background causal set using only knowledge of the
retarded Green's function. We generalize that construction to continuum
spacetimes and find that it yields a distinguished vacuum or ground state for a
non-interacting, massive or massless scalar field. This state is defined for
all compact regions and for many noncompact ones. In a static spacetime we find
that our vacuum coincides with the usual ground state. We determine it also for
a radiation-filled, spatially homogeneous and isotropic cosmos, and show that
the super-horizon correlations are approximately the same as those of a thermal
state. Finally, we illustrate the inherent non-locality of our prescription
with the example of a spacetime which sandwiches a region with curvature
in-between flat initial and final regions
A regularisation approach to causality theory for C^{1,1}Lorentzian metrics
We show that many standard results of Lorentzian causality theory remain valid if the regularity of the metric is reduced to C^{1,1}. Our approach is based on regularisations of the metric adapted to the causal structure
Conformal weights in the Kerr/CFT correspondence
It has been conjectured that a near-extreme Kerr black hole is described by a
2d CFT. Previous work has shown that CFT operators dual to axisymmetric
gravitational perturbations have integer conformal weights. In this paper, we
study the analogous problem in 5d. We consider the most general near-extreme
vacuum black hole with two rotational symmetries. This includes Myers-Perry
black holes, black rings and Kaluza-Klein black holes. We find that operators
dual to gravitational (or electromagnetic or massless scalar field)
perturbations preserving both rotational symmetries have integer conformal
weights, the same for all black holes considered.Comment: 19 page
A soliton menagerie in AdS
We explore the behaviour of charged scalar solitons in asymptotically global
AdS4 spacetimes. This is motivated in part by attempting to identify under what
circumstances such objects can become large relative to the AdS length scale.
We demonstrate that such solitons generically do get large and in fact in the
planar limit smoothly connect up with the zero temperature limit of planar
scalar hair black holes. In particular, for given Lagrangian parameters we
encounter multiple branches of solitons: some which are perturbatively
connected to the AdS vacuum and surprisingly, some which are not. We explore
the phase space of solutions by tuning the charge of the scalar field and
changing scalar boundary conditions at AdS asymptopia, finding intriguing
critical behaviour as a function of these parameters. We demonstrate these
features not only for phenomenologically motivated gravitational Abelian-Higgs
models, but also for models that can be consistently embedded into eleven
dimensional supergravity.Comment: 62 pages, 21 figures. v2: added refs and comments and updated
appendice
Counting all dyons in N =4 string theory
For dyons in heterotic string theory compactified on a six-torus, with
electric charge vector Q and magnetic charge vector P, the positive integer I =
g.c.d.(Q \wedge P) is an invariant of the U-duality group. We propose the
microscopic theory for computing the spectrum of all dyons for all values of I,
generalizing earlier results that exist only for the simplest case of I=1. Our
derivation uses a combination of arguments from duality, 4d-5d lift, and a
careful analysis of fermionic zero modes. The resulting degeneracy agrees with
the black hole degeneracy for large charges and with the degeneracy of
field-theory dyons for small charges. It naturally satisfies several physical
requirements including integrality and duality invariance. As a byproduct, we
also derive the microscopic (0,4) superconformal field theory relevant for
computing the spectrum of five-dimensional Strominger-Vafa black holes in ALE
backgrounds and count the resulting degeneracies
On defining the Hamiltonian beyond quantum theory
Energy is a crucial concept within classical and quantum physics. An
essential tool to quantify energy is the Hamiltonian. Here, we consider how to
define a Hamiltonian in general probabilistic theories, a framework in which
quantum theory is a special case. We list desiderata which the definition
should meet. For 3-dimensional systems, we provide a fully-defined recipe which
satisfies these desiderata. We discuss the higher dimensional case where some
freedom of choice is left remaining. We apply the definition to example toy
theories, and discuss how the quantum notion of time evolution as a phase
between energy eigenstates generalises to other theories.Comment: Authors' accepted manuscript for inclusion in the Foundations of
Physics topical collection on Foundational Aspects of Quantum Informatio
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