111 research outputs found
Dynamical Breakdown of Symmetry in a (2+1) Dimensional Model Containing the Chern-Simons Field
We study the vacuum stability of a model of massless scalar and fermionic
fields minimally coupled to a Chern-Simons field. The classical Lagrangian only
involves dimensionless parameters, and the model can be thought as a (2+1)
dimensional analog of the Coleman-Weinberg model. By calculating the effective
potential, we show that dynamical symmetry breakdown occurs in the two-loop
approximation. The vacuum becomes asymmetric and mass generation, for the boson
and fermion fields takes place. Renormalization group arguments are used to
clarify some aspects of the solution.Comment: Minor modifications in the text and figure
Operator Regularization and Large Noncommutative Chern Simons Theory
We examine noncommutative Chern Simons theory using operator regularization.
Both the zeta-function and the eta-function are needed to determine one loop
effects. The contributions to these functions coming from the two point
function is evaluated. The U(N) noncommutative model smoothly reduces to the
SU(N) commutative model as the noncommutative parameter theta_{mu nu} vanishes
Accelerated Universe from Gravity Leaking to Extra Dimensions
We discuss the idea that the accelerated Universe could be the result of the
gravitational leakage into extra dimensions on Hubble distances rather than the
consequence of non-zero cosmological constant.Comment: 20 pages, 6 figure
Two-Loop Quantum Corrections of Scalar QED with Non-Minimal Chern-Simons Coupling
We investigate two-loop quantum corrections to non-minimally coupled
Maxwell-Chern-Simons theory. The non-minimal gauge interaction represents the
magnetic moment interaction between the charged scalar and the electromagnetic
field. We show that the one-loop renormalizability of the theory found in
previous work does not survive to the two-loop level. However, with an
appropriate choice of the non-minimal coupling constant, it is possible to
renormalize the two-loop effective potential and hence render it potentially
useful for a detailed analysis of spontaneous symmetry breaking induced by
radiative corrections.Comment: 29 pages, including 21 figures. One author added, some formulae
corrected and references adde
Off-Diagonal Elements of the DeWitt Expansion from the Quantum Mechanical Path Integral
The DeWitt expansion of the matrix element M_{xy} = \left\langle x \right|
\exp -[\case{1}{2} (p-A)^2 + V]t \left| y \right\rangle, in
powers of can be made in a number of ways. For (the case of interest
when doing one-loop calculations) numerous approaches have been employed to
determine this expansion to very high order; when (relevant for
doing calculations beyond one-loop) there appear to be but two examples of
performing the DeWitt expansion. In this paper we compute the off-diagonal
elements of the DeWitt expansion coefficients using the Fock-Schwinger gauge.
Our technique is based on representing by a quantum mechanical path
integral. We also generalize our method to the case of curved space, allowing
us to determine the DeWitt expansion of \tilde M_{xy} = \langle x| \exp
\case{1}{2} [\case{1}{\sqrt {g}} (\partial_\mu - i
A_\mu)g^{\mu\nu}{\sqrt{g}}(\partial_\nu - i A_\nu) ] t| y \rangle by use of
normal coordinates. By comparison with results for the DeWitt expansion of this
matrix element obtained by the iterative solution of the diffusion equation,
the relative merit of different approaches to the representation of as a quantum mechanical path integral can be assessed. Furthermore, the
exact dependence of on some geometric scalars can be
determined. In two appendices, we discuss boundary effects in the
one-dimensional quantum mechanical path integral, and the curved space
generalization of the Fock-Schwinger gauge.Comment: 16pp, REVTeX. One additional appendix concerning end-point effects
for finite proper-time intervals; inclusion of these effects seem to make our
results consistent with those from explicit heat-kernel method
Spherically symmetric spacetimes in massive gravity
We explore spherically symmetric stationary solutions, generated by ``stars''
with regular interiors, in purely massive gravity. We reexamine the claim that
the resummation of non-linear effects can cure, in a domain near the source,
the discontinuity exhibited by the linearized theory as the mass m of the
graviton tends to zero. First, we find analytical difficulties with this claim,
which appears not to be robust under slight changes in the form of the mass
term. Second, by numerically exploring the inward continuation of the class of
asymptotically flat solutions, we find that, when m is ``small'', they all end
up in a singularity at a finite radius, well outside the source, instead of
joining some conjectured ``continuous'' solution near the source. We reopen,
however, the possibility of reconciling massive gravity with phenomenology by
exhibiting a special class of solutions, with ``spontaneous symmetry breaking''
features, which are close, near the source, to general relativistic solutions
and asymptote, for large radii, a de Sitter solution of curvature ~m^2.Comment: 57 pages, references addde
Mass and Gauge Invariance IV (Holography for the Karch-Randall Model)
We argue that the Karch-Randall compactification is holographically dual to a
4-d conformal field theory coupled to gravity on Anti de Sitter space. Using
this interpretation we recover the mass spectrum of the model. In particular,
we find no massless spin-2 states. By giving a purely 4-d interpretation to the
compactification we make clear that it represents the first example of a local
4-d field theory in which general covariance does not imply the existence of a
massless graviton. We also discuss some variations of the Karch-Randall model
discussed in the literature, and we examine whether its properties are generic
to all conformal field theory.Comment: 26 pages, uses package latexsym. Note added in proo
A Massive Renormalizable Abelian Gauge Theory in 2+1 Dimensions
The standard formulation of a massive Abelian vector field in
dimensions involves a Maxwell kinetic term plus a Chern-Simons mass term; in
its place we consider a Chern-Simons kinetic term plus a Stuekelberg mass term.
In this latter model, we still have a massive vector field, but now the
interaction with a charged spinor field is renormalizable (as opposed to super
renormalizable). By choosing an appropriate gauge fixing term, the Stuekelberg
auxiliary scalar field decouples from the vector field. The one-loop spinor
self energy is computed using operator regularization, a technique which
respects the three dimensional character of the antisymmetric tensor
. This method is used to evaluate the vector self
energy to two-loop order; it is found to vanish showing that the beta function
is zero to two-loop order. The canonical structure of the model is examined
using the Dirac constraint formalism.Comment: LaTeX, 17 pages, expanded reference list and discussion of
relationship to previous wor
Nonperturbative Continuity in Graviton Mass versus Perturbative Discontinuity
We address the question whether a graviton could have a small nonzero mass.
The issue is subtle for two reasons: there is a discontinuity in the mass in
the lowest tree-level approximation, and, moreover, the nonlinear
four-dimensional theory of a massive graviton is not defined unambiguously.
First, we reiterate the old argument that for the vanishing graviton mass the
lowest tree-level approximation breaks down since the higher order corrections
are singular in the graviton mass. However, there exist nonperturbative
solutions which correspond to the summation of the singular terms and these
solutions are continuous in the graviton mass. Furthermore, we study a
completely nonlinear and generally covariant five-dimensional model which
mimics the properties of the four-dimensional theory of massive gravity. We
show that the exact solutions of the model are continuous in the mass, yet the
perturbative expansion exhibits the discontinuity in the leading order and the
singularities in higher orders as in the four-dimensional case. Based on exact
cosmological solutions of the model we argue that the helicity-zero graviton
state which is responsible for the perturbative discontinuity decouples from
the matter in the limit of vanishing graviton mass in the full classical
theory.Comment: Phys Rev D version, 21 pages, 1 figure, a reference and some
clarifications are added, typos correcte
Graviton and scalar propagations on AdS(4) space in f(R) gravities
We investigate propagations of graviton and additional scalar on
four-dimensional anti de Sitter (AdS) space using gravity models
with external sources. It is shown that there is the van Dam-Veltman-Zakharov
(vDVZ) discontinuity in gravity models because gravity implies GR
with additional scalar. This indicates a difference between general relativity
and gravity clearly.Comment: 11 pages, no figures, version to appear in EPJ
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