66 research outputs found
A 2D integrable axion model and Target space duality
A review is given on the recently proposed two dimensional axion model (O(3)
sigma-model with a dynamical Hopf-term) and the T-duality relating it to the
SU(2)xU(1) symmetric anisotropic sigma-model. Strong evidence is presented for
the correctness of the proposed S-matrix for both models comparing perturbative
and Thermodynamical Bethe Ansatz calculations for different types of free
energies. This also provides a very stringent test of the validity of T-duality
transformation at the quantum level. The quantum non-integrability of the O(3)
sigma-model with a non-dynamical Hopf-term, in contradistinction to the axion
model, is illustrated by calculating the 2-->3 particle production amplitude to
lowest order.Comment: LateX, 21 pages, 1 figure. Improved version of a talk delivered at
the Johns Hopkins workshop `Non-perturbative QFT Methods and their
Applications', Budapest, 200
Classification of Static, Spherically Symmetric Solutions of the Einstein-Yang-Mills Theory with Positive Cosmological Constant
We give a complete classification of all static, spherically symmetric
solutions of the SU(2) Einstein-Yang-Mills theory with a positive cosmological
constant. Our classification proceeds in two steps. We first extend solutions
of the radial field equations to their maximal interval of existence. In a
second step we determine the Carter-Penrose diagrams of all 4-dimensional
space-times constructible from such radial pieces. Based on numerical studies
we sketch a complete phase space picture of all solutions with a regular
origin.Comment: 49 pages, 19 figures, submitted to Commun. Math. Phy
Spatially Compact Solutions and Stabilization in Einstein-Yang-Mills-Higgs Theories
New solutions to the static, spherically symmetric Einstein-Yang-Mills-Higgs
equations with the Higgs field in the triplet resp. doublet representation are
presented. They form continuous families parametrized by
( resp. denoting the W-boson resp. the Planck mass). The
corresponding spacetimes are regular and have spatially compact sections. A
particularly interesting class with the Yang-Mills amplitude being nodeless is
exhibited and is shown to be linearly stable with respect to spherically
symmetric perturbations. For some solutions with nodes of the Yang-Mills
amplitude a new stabilization phenomenon is found, according to which their
unstable modes disappear as increases (for the triplet) or decreases
(for the doublet).Comment: 7 pages, 4 figure
Non-Abelian Vortices with a Twist
Non-Abelian flux-tube (string) solutions carrying global currents are found
in the bosonic sector of 4-dimensional N=2 super-symmetric gauge theories. The
specific model considered here posseses U(2)local x SU(2)global symmetry, with
two scalar doublets in the fundamental representation of SU(2). We construct
string solutions that are stationary and translationally symmetric along the x3
direction, and they are characterized by a matrix phase between the two
doublets, referred to as "twist". Consequently, twisted strings have nonzero
(global) charge, momentum, and in some cases even angular momentum per unit
length. The planar cross section of a twisted string corresponds to a
rotationally symmetric, charged non-Abelian vortex, satisfying 1st order
Bogomolny-type equations and 2nd order Gauss-constraints. Interestingly,
depending on the nature of the matrix phase, some of these solutions even break
rotational symmetry in R3. Although twisted vortices have higher energy than
the untwisted ones, they are expected to be linearly stable since one can
maintain their charge (or twist) fixed with respect to small perturbations.Comment: 18 pages, 5 figure
Stability Analysis of Superconducting Electroweak Vortices
We carry out a detailed stability analysis of the superconducting vortex
solutions in the Weinberg-Salam theory described in Nucl.Phys. B826 (2010) 174.
These vortices are characterized by constant electric current and electric
charge density , for they reduce to Z strings. We consider the
generic field fluctuations around the vortex and apply the functional Jacobi
criterion to detect the negative modes in the fluctuation operator spectrum. We
find such modes and determine their dispersion relation, they turn out to be of
two different types, according to their spatial behavior. There are
non-periodic in space negative modes, which can contribute to the instability
of infinitely long vortices, but they can be eliminated by imposing the
periodic boundary conditions along the vortex. There are also periodic negative
modes, but their wavelength is always larger than a certain minimal value, so
that they cannot be accommodated by the short vortex segments. However, even
for the latter there remains one negative mode responsible for the homogeneous
expansion instability. This mode may probably be eliminated when the vortex
segment is bent into a loop. This suggests that small vortex loops balanced
against contraction by the centrifugal force could perhaps be stable.Comment: 42 pages, 11 figure
Quantum mechanics of an electron in a homogeneous magnetic field and a singular magnetic flux tube
The eigenvalue problem of the Hamiltonian of an electron confined to a plane
and subjected to a perpendicular time-independent magnetic field which is the
sum of a homogeneous field and an additional field contributed by a singular
flux tube, i.e. of zero width, is investigated. Since both a direct approach
based on distribution-valued operators and a limit process starting from a
non-singular flux tube, i.e. of finite size, fail, an alternative method is
applied leading to consistent results. An essential feature is quantum
mechanical supersymmetry at g=2 which imposes, by proper representation, the
correct choice of "boundary conditions". The corresponding representation of
the Hilbert space in coordinate space differs from the usual space of
square-integrable 2-spinors, entailing other unusual properties. The analysis
is extended to so that supersymmetry is explicitly broken. Finally,
the singular Aharonov-Bohm system with the same amount of singular flux is
analysed by making use of the fact that the Hilbert space must be the same.Comment: 23 pages, LaTeX, minor change
The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant
Liouville theory is shown to describe the asymptotic dynamics of
three-dimensional Einstein gravity with a negative cosmological constant. This
is because (i) Chern-Simons theory with a gauge group
on a space-time with a cylindrical boundary is equivalent to the non-chiral
WZW model; and (ii) the anti-de Sitter boundary conditions implement
the constraints that reduce the WZW model to the Liouville theory.Comment: 10 pages in LaTeX, LaTeX problem fixe
Superconducting non-Abelian vortices in Weinberg-Salam theory -- electroweak thunderbolts
We present a detailed analysis of classical solutions in the bosonic sector
of the electroweak theory which describe vortices carrying a constant electric
current . These vortices exist for any value of the Higgs boson mass
and for any weak mixing angle, and in the zero current limit they reduce to Z
strings. Their current is produced by the condensate of vector W bosons and
typically it can attain billions of Amperes. For large the vortices
show a compact condensate core of size , embedded into a
region of size where the electroweak gauge symmetry is
completely restored, followed by a transition zone where the Higgs field
interpolates between the symmetric and broken phases. Outside this zone the
fields are the same as for the ordinary electric wire. An asymptotic
approximation of the large solutions suggests that the current can
be {arbitrarily} large, due to the scale invariance of the vector boson
condensate. Finite vortex segments whose length grows with seem to
be perturbatively stable. This suggests that they can transfer electric charge
between different regions of space, similarly to thunderbolts. It is also
possible that they can form loops stabilized by the centrifugal force --
electroweak vortons.Comment: 83 pages, 25 figure
Fixed points of quantum gravity in extra dimensions
We study quantum gravity in more than four dimensions with renormalisation
group methods. We find a non-trivial ultraviolet fixed point in the
Einstein-Hilbert action. The fixed point connects with the perturbative
infrared domain through finite renormalisation group trajectories. We show that
our results for fixed points and related scaling exponents are stable. If this
picture persists at higher order, quantum gravity in the metric field is
asymptotically safe. We discuss signatures of the gravitational fixed point in
models with low-scale gravity and compact extra dimensions.Comment: Wording sharpened, refs added, to appear in PL
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