58 research outputs found
A New Family of Gauges in Linearized General Relativity
For vacuum Maxwell theory in four dimensions, a supplementary condition
exists (due to Eastwood and Singer) which is invariant under conformal
rescalings of the metric, in agreement with the conformal symmetry of the
Maxwell equations. Thus, starting from the de Donder gauge, which is not
conformally invariant but is the gravitational counterpart of the Lorenz gauge,
one can consider, led by formal analogy, a new family of gauges in general
relativity, which involve fifth-order covariant derivatives of metric
perturbations. The admissibility of such gauges in the classical theory is
first proven in the cases of linearized theory about flat Euclidean space or
flat Minkowski space-time. In the former, the general solution of the equation
for the fulfillment of the gauge condition after infinitesimal diffeomorphisms
involves a 3-harmonic 1-form and an inverse Fourier transform. In the latter,
one needs instead the kernel of powers of the wave operator, and a contour
integral. The analysis is also used to put restrictions on the dimensionless
parameter occurring in the DeWitt supermetric, while the proof of admissibility
is generalized to a suitable class of curved Riemannian backgrounds.
Eventually, a non-local construction is obtained of the tensor field which
makes it possible to achieve conformal invariance of the above gauges.Comment: 28 pages, plain Tex. In the revised version, sections 4 and 5 are
completely ne
Back reaction of vacuum and the renormalization group flow from the conformal fixed point
We consider the GUT-like model with two scalar fields which has infinitesimal
deviation from the conformal invariant fixed point at high energy region. In
this case the dominating quantum effect is the conformal trace anomaly and the
interaction between the anomaly-generated propagating conformal factor of the
metric and the usual dimensional scalar field. This interaction leads to the
renormalization group flow from the conformal point. In the supersymmetric
conformal invariant model such an effect produces a very weak violation of
sypersymmetry at lower energies.Comment: 15 pages, LaTex, ten figures, uuencoded fil
Conformally invariant bending energy for hypersurfaces
The most general conformally invariant bending energy of a closed
four-dimensional surface, polynomial in the extrinsic curvature and its
derivatives, is constructed. This invariance manifests itself as a set of
constraints on the corresponding stress tensor. If the topology is fixed, there
are three independent polynomial invariants: two of these are the
straighforward quartic analogues of the quadratic Willmore energy for a
two-dimensional surface; one is intrinsic (the Weyl invariant), the other
extrinsic; the third invariant involves a sum of a quadratic in gradients of
the extrinsic curvature -- which is not itself invariant -- and a quartic in
the curvature. The four-dimensional energy quadratic in extrinsic curvature
plays a central role in this construction.Comment: 16 page
Quantum Interaction : the Construction of Quantum Field defined as a Bilinear Form
We construct the solution of the quantum wave equation
as a bilinear form which can
be expanded over Wick polynomials of the free -field, and where
is defined as the normal ordered product with
respect to the free -field. The constructed solution is correctly defined
as a bilinear form on , where is a
dense linear subspace in the Fock space of the free -field. On
the diagonal Wick symbol of this bilinear form
satisfies the nonlinear classical wave equation.Comment: 32 pages, LaTe
Logarithmic correction to BH entropy as Noether charge
We consider the role of the type-A trace anomaly in static black hole
solutions to semiclassical Einstein equation in four dimensions. Via Wald's
Noether charge formalism, we compute the contribution to the entropy coming
from the anomaly induced effective action and unveil a logarithmic correction
to the Bekenstein-Hawking area law.
The corrected entropy is given by a seemingly universal formula involving the
coefficient of the type-A trace anomaly, the Euler characteristic of the
horizon and the value at the horizon of the solution to the uniformization
problem for Q-curvature. Two instances are examined in detail: Schwarzschild
and a four-dimensional massless topological black hole. We also find agreement
with the logarithmic correction due to one-loop contribution of conformal
fields in the Schwarzschild background.Comment: 14 pages, JHEP styl
Causal structures and causal boundaries
We give an up-to-date perspective with a general overview of the theory of
causal properties, the derived causal structures, their classification and
applications, and the definition and construction of causal boundaries and of
causal symmetries, mostly for Lorentzian manifolds but also in more abstract
settings.Comment: Final version. To appear in Classical and Quantum Gravit
C T for higher derivative conformal fields and anomalies of (1, 0) superconformal 6d theories
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