896 research outputs found
Spectral Action for Robertson-Walker metrics
We use the Euler-Maclaurin formula and the Feynman-Kac formula to extend our
previous method of computation of the spectral action based on the Poisson
summation formula. We show how to compute directly the spectral action for the
general case of Robertson-Walker metrics. We check the terms of the expansion
up to a_6 against the known universal formulas of Gilkey and compute the
expansion up to a_{10} using our direct method
Gravity, Non-Commutative Geometry and the Wodzicki Residue
We derive an action for gravity in the framework of non-commutative geometry
by using the Wodzicki residue. We prove that for a Dirac operator on an
dimensional compact Riemannian manifold with , even, the Wodzicki
residue Res is the integral of the second coefficient of the heat
kernel expansion of . We use this result to derive a gravity action for
commutative geometry which is the usual Einstein Hilbert action and we also
apply our results to a non-commutative extension which, is given by the tensor
product of the algebra of smooth functions on a manifold and a finite
dimensional matrix algebra. In this case we obtain gravity with a cosmological
constant.Comment: 17p., MZ-TH/93-3
Massive Hermitian Gravity
Einstein-Strauss Hermitian gravity was recently formulated as a gauge theory
where the tangent group is taken to be the pseudo-unitary group instead of the
orthogonal group. A Higgs mechanism for massive gravity was also formulated. We
generalize this construction to obtain massive Hermitian gravity with the use
of a complex Higgs multiplet. We show that both the graviton and antisymmetric
tensor acquire the same mass. At the linearized level, the theory is ghost free
around Minkowski background and describes a massive graviton with five degrees
of freedom and an antisymmetric field with three degrees of of freedom. We
determine the strong coupling scales for these degrees of freedom and argue
that the potential nonlinear ghosts, if they exist, have to decouple from the
gravitational degrees of freedom in strong coupling regime.Comment: 10 page
Differential Algebras in Non-Commutative Geometry
We discuss the differential algebras used in Connes' approach to Yang-Mills
theories with spontaneous symmetry breaking. These differential algebras
generated by algebras of the form functions matrix are shown to be
skew tensorproducts of differential forms with a specific matrix algebra. For
that we derive a general formula for differential algebras based on tensor
products of algebras. The result is used to characterize differential algebras
which appear in models with one symmetry breaking scale.Comment: 21 page
Resilience of the Spectral Standard Model
We show that the inconsistency between the spectral Standard Model and the
experimental value of the Higgs mass is resolved by the presence of a real
scalar field strongly coupled to the Higgs field. This scalar field was already
present in the spectral model and we wrongly neglected it in our previous
computations. It was shown recently by several authors, independently of the
spectral approach, that such a strongly coupled scalar field stabilizes the
Standard Model up to unification scale in spite of the low value of the Higgs
mass. In this letter we show that the noncommutative neutral singlet modifies
substantially the RG analysis, invalidates our previous prediction of Higgs
mass in the range 160--180 Gev, and restores the consistency of the
noncommutative geometric model with the low Higgs mass.Comment: 13 pages, more contours added to Higgs mass plot, one reference adde
Non-Commutative Geometry and Chiral Perturbation Lagrangian
Chiral perturbation lagrangian in the framework of non-commutative geometry
is considered in full detail. It is found that the explicit symmetry breaking
terms appear and some relations between the coupling constants of the theory
come out naturally. The WZW term also turns up on the same footing as the other
terms of the chiral lagrangian.Comment: Latex, 9 page
Massive Gravity Simplified: A Quadratic Action
We present a simplified formulation of massive gravity where the Higgs fields
have quadratic kinetic term. This new formulation allows us to prove in a very
explicit way that all massive gravity theories considered so far inevitably
have Boulware-Deser ghost in non-trivial fluctuations of background metric.Comment: 8 pages, paragraph added proving that Bianchi identity does not imply
vanishing of linearized curvatur
SL(2,C) Gravity with Complex Vierbein and Its Noncommutative Extension
We show that it is possible to formulate gravity with a complex vierbein
based on SL(2,C) gauge invariance. The proposed action is a four-form where the
metric is not introduced but results as a function of the complex vierbein.
This formulation is based on the first order formalism. The novel feature here
is that integration of the spin-connection gauge field gives rise to kinetic
terms for a massless graviton, a massive graviton with the Fierz-Pauli mass
term, and a scalar field. The resulting theory is equivalent to bigravity. We
then show that by extending the gauge group to GL(2,C} the formalism can be
easily generalized to apply to a noncommutative space with the star product. We
give the deformed action and derive the Seiberg-Witten map for the complex
vierbein and gauge fields.Comment: Minor corrections. The noncommutative action in section 3 is
simplified. Version to appear in Physical Review
A survey of spectral models of gravity coupled to matter
This is a survey of the historical development of the Spectral Standard Model
and beyond, starting with the ground breaking paper of Alain Connes in 1988
where he observed that there is a link between Higgs fields and finite
noncommutative spaces. We present the important contributions that helped in
the search and identification of the noncommutative space that characterizes
the fine structure of space-time. The nature and properties of the
noncommutative space are arrived at by independent routes and show the
uniqueness of the Spectral Standard Model at low energies and the Pati-Salam
unification model at high energies.Comment: An appendix is added to include scalar potential analysis for a
Pati-Salam model. 58 Page
Finiteness of 2D Topological BF-Theory with Matter Coupling
We study the ultraviolet and the infrared behavior of 2D topological
BF-Theory coupled to vector and scalar fields. This model is equivalent to 2D
gravity coupled to topological matter. Using techniques of the algebraic
renormalization program we show that this model is anomaly free and ultraviolet
as well as infrared finite at all orders of perturbation theory.Comment: 17 pages, Late
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