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Symmetry, gravity and noncommutativity
"... We review some aspects of the implementation of spacetime symmetries in noncommutative field theories, emphasizing their origin in string theory and how they may be used to construct theories of gravitation. The geometry of canonical noncommutative gauge transformations is analysed in detail and it ..."
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Cited by 23 (2 self)
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We review some aspects of the implementation of spacetime symmetries in noncommutative field theories, emphasizing their origin in string theory and how they may be used to construct theories of gravitation. The geometry of canonical noncommutative gauge transformations is analysed in detail and it is shown how noncommutative YangMills theory can be related to a gravity theory. The construction of twisted spacetime symmetries and their role in constructing a noncommutative extension of general relativity is described. We also analyse certain generic features of noncommutative gauge theories on Dbranes in curved spaces, treating several explicit examples of superstring backgrounds.
Noncommutative symmetries and gravity
, 2006
"... Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now starmultiplied. Consistently, spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms. Their deformed Lie algebra structure and that of infinitesimal Poincaré transf ..."
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Cited by 11 (6 self)
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Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now starmultiplied. Consistently, spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms. Their deformed Lie algebra structure and that of infinitesimal Poincaré transformations is defined and explicitly constructed. This allows to construct a noncommutative theory of gravity.
Emergent Spacetime and The Origin of Gravity
, 2009
"... We present an exposition on the geometrization of the electromagnetic force. We show that, in noncommutative (NC) spacetime, there always exists a coordinate transformation to locally eliminate the electromagnetic force, which is precisely the Darboux theorem in symplectic geometry. As a consequence ..."
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Cited by 6 (4 self)
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We present an exposition on the geometrization of the electromagnetic force. We show that, in noncommutative (NC) spacetime, there always exists a coordinate transformation to locally eliminate the electromagnetic force, which is precisely the Darboux theorem in symplectic geometry. As a consequence, the electromagnetism can be realized as a geometrical property of spacetime like gravity. We show that the geometrization of the electromagnetic force in NC spacetime is the origin of gravity, dubbed as the emergent gravity. We discuss how the emergent gravity reveals a noble, radically different picture about the origin of spacetime. In particular, the emergent gravity naturally explains the dynamical origin of flat spacetime, which is absent in Einstein gravity. This spacetime picture turns out to be crucial for a tenable solution of the cosmological constant problem.
PROJECTIVE MODULE DESCRIPTION OF EMBEDDED NONCOMMUTATIVE SPACES
, 810
"... ABSTRACT. Noncommutative differential geometry over the Moyal algebra is developed following an algebraic approach. It is then applied to investigate embedded noncommutative spaces. We explicitly construct the projective modules corresponding to the tangent bundles of the noncommutative spaces, and ..."
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Cited by 5 (3 self)
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ABSTRACT. Noncommutative differential geometry over the Moyal algebra is developed following an algebraic approach. It is then applied to investigate embedded noncommutative spaces. We explicitly construct the projective modules corresponding to the tangent bundles of the noncommutative spaces, and recover from this algebraic formulation the metric, LeviCivita connection and related curvature introduced in earlier work. Transformation rules of connections and curvatures under general coordinate changes are given explicitly. A bar involution on the Moyal algebra is discovered, and its consequences on the noncommutative differential geometry are described. CONTENTS
DISTAUPO/07 Noncommutative Gravity and the ⋆Lie algebra of diffeomorphisms ∗
, 2007
"... We construct functions and tensors on noncommutative spacetime by systematically twisting the corresponding commutative structures. The study of the deformed diffeomorphisms (and Poincaré) Lie algebra allows to construct a noncomutative theory of gravity. ..."
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Cited by 1 (0 self)
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We construct functions and tensors on noncommutative spacetime by systematically twisting the corresponding commutative structures. The study of the deformed diffeomorphisms (and Poincaré) Lie algebra allows to construct a noncomutative theory of gravity.
SR11001 Belgrade
, 709
"... Consider the quasicommutative approximation to a noncommutative geometry. It is shown that there is a natural map from the resulting Poisson structure to the Riemann curvature of a metric. This map is applied to the study of highfrequency gravitational radiation. In classical gravity in the WKB ap ..."
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Consider the quasicommutative approximation to a noncommutative geometry. It is shown that there is a natural map from the resulting Poisson structure to the Riemann curvature of a metric. This map is applied to the study of highfrequency gravitational radiation. In classical gravity in the WKB approximation there are two results of interest, a dispersion relation and a conservation law. Both of these results can be extended to the noncommutative case, with the difference that they result from a cocycle condition on the highfrequency contribution to the Poisson structure, not from the field equations.
Dimensional Reduction of Supersymmetric Gauge Theories
, 903
"... Main objective of the present dissertation is the determination of all the possible low energy models which emerge in four dimensions by the dimensional reduction of a gauge theory over multiple connected coset spaces. The higher dimensional gauge theory is chosen to be the one that the Heterotic st ..."
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Main objective of the present dissertation is the determination of all the possible low energy models which emerge in four dimensions by the dimensional reduction of a gauge theory over multiple connected coset spaces. The higher dimensional gauge theory is chosen to be the one that the Heterotic string theory suggests: (i) it is defined in ten dimensions, (ii) it is based on the E8 × E8 symmetry group and (iii) it is N = 1 globally supersymmetric. The search of all fourdimensional gauge theories resulting from the aforementioned dimensional reduction, is restricted only to models which are potentially interesting from a phenomenological point of view. This requirement constrain these models to come from one of the known Grand Unified Theories (GUTs) in an intermediate stage of the spontaneous symmetry breaking. Main result of my study is that extensions of the Standard Model (SM) which are based on the PatiSalam group structure can be obtained in four dimensions. A second direction of research which is discussed in this dissertation is based on the following conclusions of a previous research work: (i) It is possible to obtain fourdimensional
DISTAUPO/05 Noncommutative Symmetries and Gravity ⋆
, 2006
"... Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now starmultiplied. Consistently, spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms. Their deformed Lie algebra structure and that of infinitesimal Poincaré transf ..."
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Spacetime geometry is twisted (deformed) into noncommutative spacetime geometry, where functions and tensors are now starmultiplied. Consistently, spacetime diffeomorhisms are twisted into noncommutative diffeomorphisms. Their deformed Lie algebra structure and that of infinitesimal Poincaré transformations is defined and explicitly constructed. This allows to construct a noncommutative theory of gravity. This article is based on common work with Christian Blohmann, Marija Dimitrijević,