989 research outputs found
An Invariant Action for Noncommutative Gravity in Four-Dimensions
Two main problems face the construction of noncommutative actions for gravity
with star products: the complex metric and finding an invariant measure. The
only gauge groups that could be used with star products are the unitary groups.
I propose an invariant gravitational action in D=4 dimensions based on the
constrained gauge group U(2,2) broken to No metric is
used, thus giving a naturally invariant measure. This action is generalized to
the noncommutative case by replacing ordinary products with star products. The
four dimensional noncommutative action is studied and the deformed action to
first order in deformation parameter is computed.Comment: 11 pages. Paper shortened. Consideration is now limited to gravity in
four-dimension
The Spectral Action for Dirac Operators with skew-symmetric Torsion
We derive a formula for the gravitational part of the spectral action for
Dirac operators on 4-dimensional manifolds with totally anti-symmetric torsion.
We find that the torsion becomes dynamical and couples to the traceless part of
the Riemann curvature tensor. Finally we deduce the Lagrangian for the Standard
Model of particle physics in presence of torsion from the Chamseddine-Connes
Dirac operator.Comment: Longer introduction and conclusion adde
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
Gravity with de Sitter and Unitary Tangent Groups
Einstein Gravity can be formulated as a gauge theory with the tangent space
respecting the Lorentz symmetry. In this paper we show that the dimension of
the tangent space can be larger than the dimension of the manifold and by
requiring the invariance of the theory with respect to 5d Lorentz group (de
Sitter group) Einstein theory is reproduced unambiguously. The other
possibility is to have unitary symmetry on a complex tangent space of the same
dimension as the manifold. In this case the resultant theory is
Einstein-Strauss Hermitian gravity. The tangent group is important for matter
couplings. We show that in the de Sitter case the 4 dimensional space time
vector and scalar are naturally unified by a hidden symmetry being components
of a 5d vector in the tangent space. With a de Sitter tangent group spinors can
exist only when they are made complex or taken in doublets in a way similar to
N=2 supersymmetry.Comment: 23 pages, one reference added.To be published in JHE
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
Metrics Admitting Killing Spinors In Five Dimensions
BPS black hole configurations which break half of supersymmetry in the theory
of N=2, d=5 supergravity coupled to an arbitrary number of abelian vector
multiplets are discussed. A general class of solutions comprising all known BPS
rotating black hole solutions is obtained.Comment: 15 pages, Late
SO(10) unification in noncommutative geometry revisited
We investigate the SO(10)-unification model in a Lie algebraic formulation of
noncommutative geometry. The SO(10)-symmetry is broken by a 45-Higgs and the
Majorana mass term for the right neutrinos (126-Higgs) to the standard model
structure group. We study the case that the fermion masses are as general as
possible, which leads to two 10-multiplets, four 120-multiplets and two
additional 126-multiplets of Higgs fields. This Higgs structure differs
considerably from the two Higgs multiplets 16 \otimes 16^* and 16^c \otimes
16^* used by Chamseddine and Fr\"ohlich. We find the usual tree-level
predictions of noncommutative geometry m_W=(1/2)m_t, \sin^2\theta_W=(3/8) and
g_2=g_3 as well as m_H \leq m_t.Comment: 25 pages, LaTeX 2e. v2: typos corrected and footnote on
Super-Kamiokande results adde
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