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337
Noncommutative geometry and gravity
"... We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a starproduct. The class of noncommutative spaces studied is very rich. Nonanti ..."
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Cited by 77 (18 self)
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We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a starproduct. The class of noncommutative spaces studied is very rich. Nonanticommutative superspaces are also briefly considered. The differential geometry developed is covariant under deformed diffeomorphisms and it is coordinate independent. The main target of this work is the construction of Einstein’s equations for gravity on noncommutative manifolds.
General properties of noncommutative field theories,” Nucl
 Phys. B
, 2000
"... In this paper we study general properties of noncommutative field theories obtained from the SeibergWitten limit of string theories in the presence of an external Bfield. We analyze the extension of the Wightman axioms to this context and explore their consequences, in particular we present a proo ..."
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Cited by 74 (3 self)
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In this paper we study general properties of noncommutative field theories obtained from the SeibergWitten limit of string theories in the presence of an external Bfield. We analyze the extension of the Wightman axioms to this context and explore their consequences, in particular we present a proof of the CPT theorem for theories with spacespace noncommutativity. We analyze as well questions associated to the spinstatistics connections, and show that noncommutative N = 4, U(1) gauge theory can be softly broken to N = 0 satisfying the axioms and providing an example where the Wilsonian low energy effective action can be constructed without UV/IR problems, after a judicious choice of soft breaking parameters is made. We also assess the phenomenological prospects of such a theory, which are in fact rather negative. 1
Emergent Gravity from Noncommutative Gauge Theory
, 2007
"... We show that the matrixmodel action for noncommutative U(n) gauge theory actually describes SU(n) gauge theory coupled to gravity. This is elaborated in the 4dimensional case. The SU(n) gauge fields as well as additional scalar fields couple to an effective metric Gab, which is determined by a dyn ..."
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Cited by 61 (29 self)
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We show that the matrixmodel action for noncommutative U(n) gauge theory actually describes SU(n) gauge theory coupled to gravity. This is elaborated in the 4dimensional case. The SU(n) gauge fields as well as additional scalar fields couple to an effective metric Gab, 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.
Ultraviolet Finite Quantum Field Theory on Quantum
 Spacetime, Comm. Math. Phys
"... Dedicated to Rudolf Haag on the occasion of his 80 th birthday. We discuss a formulation of quantum field theory on quantum space time where the perturbation expansion of the Smatrix is term by term ultraviolet finite. The characteristic feature of our approach is a quantum version of the Wick prod ..."
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Cited by 53 (12 self)
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Dedicated to Rudolf Haag on the occasion of his 80 th birthday. We discuss a formulation of quantum field theory on quantum space time where the perturbation expansion of the Smatrix is term by term ultraviolet finite. The characteristic feature of our approach is a quantum version of the Wick product at coinciding points: the differences of coordinates qj − qk are not set equal to zero, which would violate the commutation relation between their components. We show that the optimal degree of approximate coincidence can be defined by the evaluation of a conditional expectation which replaces each function of qj − qk by its expectation value in opti(q1 + · · ·+qn) mally localized states, while leaving the mean coordinates 1 n invariant. The resulting procedure is to a large extent unique, and is invariant under translations and rotations, but violates Lorentz invariance. Indeed, optimal localization refers to a specific Lorentz frame, where the electric and magnetic parts of the commutator of the coordinates have to coincide [11]. Employing an adiabatic switching, we show that the Smatrix is term by term finite. The matrix elements of the transfer matrix are determined, at each order in the perturbative expansion, by kernels with Gaussian decay in the Planck scale. The adiabatic limit and the large scale limit of this theory will be studied elsewhere. 1
Untwisting noncommutative R d and the equivalence of quantum field theories
 Nucl.Phys. B
, 2000
"... We show that there is a duality exchanging noncommutativity and nontrivial statistics for quantum field theory on R d. Employing methods of quantum groups, we observe that ordinary and noncommutative R d are related by twisting. We extend the twist to an equivalence for quantum field theory using t ..."
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Cited by 44 (1 self)
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We show that there is a duality exchanging noncommutativity and nontrivial statistics for quantum field theory on R d. Employing methods of quantum groups, we observe that ordinary and noncommutative R d are related by twisting. We extend the twist to an equivalence for quantum field theory using the framework of braided quantum field theory. The twist exchanges both commutativity with noncommutativity and ordinary with nontrivial statistics. The same holds for the noncommutative torus.
Renormalization of Noncommutative YangMills Theories: A Simple Example
, 2000
"... We prove by explicit calculation that Feynman graphs in noncommutative YangMills theory made of repeated insertions into itself of arbitrarily many oneloop ghost propagator corrections are renormalizable by local counterterms. This provides a strong support for the renormalizability conjecture of ..."
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Cited by 35 (4 self)
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We prove by explicit calculation that Feynman graphs in noncommutative YangMills theory made of repeated insertions into itself of arbitrarily many oneloop ghost propagator corrections are renormalizable by local counterterms. This provides a strong support for the renormalizability conjecture of that model.