171 research outputs found
5d/4d U-dualities and N=8 black holes
We use the connection between the U-duality groups in d=5 and d=4 to derive
properties of the N=8 black hole potential and its critical points
(attractors). This approach allows to study and compare the supersymmetry
features of different solutions.Comment: 23 pages, LaTeX; some notations cleared up; final version on Phys.
Rev.
Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
We derive noncommutative Einstein equations for abelian twists and their
solutions in consistently symmetry reduced sectors, corresponding to twisted
FRW cosmology and Schwarzschild black holes. While some of these solutions must
be rejected as models for physical spacetimes because they contradict
observations, we find also solutions that can be made compatible with low
energy phenomenology, while exhibiting strong noncommutativity at very short
distances and early times.Comment: LaTeX 12 pages, JHEP.st
Noncommutative Symmetries and Gravity
Spacetime geometry is twisted (deformed) into noncommutative spacetime
geometry, where functions and tensors are now star-multiplied. Consistently,
spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms. Their
deformed Lie algebra structure and that of infinitesimal Poincare'
transformations is defined and explicitly constructed.
This allows to construct a noncommutative theory of gravity.Comment: 26 pages. Lectures given at the workshop `Noncommutative Geometry in
Field and String Theories', Corfu Summer Institute on EPP, September 2005,
Corfu, Greece. Version 2: Marie Curie European Reintegration Grant
MERG-CT-2004-006374 acknowledge
R-Matrix Formulation of the Quantum Inhomogeneous Groups Iso_qr(N) and Isp_qr(N)
The quantum commutations and the orthogonal (symplectic) conditions
for the inhomogeneous multiparametric -groups of the type are
found in terms of the -matrix of . A consistent
Hopf structure on these inhomogeneous -groups is constructed by means of a
projection from . Real forms are discussed: in
particular we obtain the -groups , including the quantum
Poincar\'e group.Comment: 14 pages, latex, no figure
Quantum Principal Bundles on Projective Bases
The purpose of this paper is to propose a sheaf theoretic approach to the theory of quantum principal bundles over non affine bases. We study noncommutative principal bundles corresponding to G→ G/ P, where G is a semisimple group and P a parabolic subgroup
Noncommutative Solitons of Gravity
We investigate a three-dimensional gravitational theory on a noncommutative
space which has a cosmological constant term only. We found various kinds of
nontrivial solutions, by applying a similar technique which was used to seek
noncommutative solitons in noncommutative scalar field theories. Some of those
solutions correspond to bubbles of spacetimes, or represent dimensional
reduction. The solution which interpolates and Minkowski metric
is also found. All solutions we obtained are non-perturbative in the
noncommutative parameter , therefore they are different from solutions
found in other contexts of noncommutative theory of gravity and would have a
close relation to quantum gravity.Comment: 29 pages, 5 figures. v2: minor corrections done in Section 3.1 and
Appendix, references added. v3, v4: typos correcte
Duality and Braiding in Twisted Quantum Field Theory
We re-examine various issues surrounding the definition of twisted quantum
field theories on flat noncommutative spaces. We propose an interpretation
based on nonlocal commutative field redefinitions which clarifies previously
observed properties such as the formal equivalence of Green's functions in the
noncommutative and commutative theories, causality, and the absence of UV/IR
mixing. We use these fields to define the functional integral formulation of
twisted quantum field theory. We exploit techniques from braided tensor algebra
to argue that the twisted Fock space states of these free fields obey
conventional statistics. We support our claims with a detailed analysis of the
modifications induced in the presence of background magnetic fields, which
induces additional twists by magnetic translation operators and alters the
effective noncommutative geometry seen by the twisted quantum fields. When two
such field theories are dual to one another, we demonstrate that only our
braided physical states are covariant under the duality.Comment: 35 pages; v2: Typos correcte
Nonassociative geometry in quasi-Hopf representation categories II: connections and curvature
We continue our systematic development of noncommutative and nonassociative differential geometry internal to the representation category of a quasitriangular quasi-Hopf algebra. We describe derivations, differential operators, differential calculi and connections using universal categorical constructions to capture algebraic properties such as Leibniz rules. Our main result is the construction of morphisms which provide prescriptions for lifting connections to tensor products and to internal homomorphisms. We describe the curvatures of connections within our formalism, and also the formulation of Einstein-Cartan geometry as a putative framework for a nonassociative theory of gravity
Gauge field theories with covariant star-product
A noncommutative gauge theory is developed using a covariant star-product
between differential forms defined on a symplectic manifold, considered as the
space-time. It is proven that the field strength two-form is gauge covariant
and satisfies a deformed Bianchi identity. The noncommutative Yang-Mills action
is defined using a gauge covariant metric on the space-time and its gauge
invariance is proven up to the second order in the noncommutativity parameter.Comment: Dedicated to Ioan Gottlieb on the occasion of his 80th birthday
anniversary. 12 page
Emergent Gravity from Noncommutative Gauge Theory
We show that the matrix-model action for noncommutative U(n) gauge theory
actually describes SU(n) gauge theory coupled to gravity. This is elaborated in
the 4-dimensional case. The SU(n) gauge fields as well as additional scalar
fields couple to an effective metric G_{ab}, which is determined by a dynamical
Poisson structure. The emergent gravity is intimately related to
noncommutativity, encoding those degrees of freedom which are usually
interpreted as U(1) gauge fields. This leads to a class of metrics which
contains the physical degrees of freedom of gravitational waves, and allows to
recover e.g. the Newtonian limit with arbitrary mass distribution. It also
suggests a consistent picture of UV/IR mixing in terms of an induced gravity
action. This should provide a suitable framework for quantizing gravity.Comment: 28 pages + 11 pages appendix. V2: references and discussion added.
V3: minor correctio
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