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A Gravity Theory on Noncommutative Spaces

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arxiv hep-th/0504183 v3 pith:ZG2L7PDS submitted 2005-04-22 hep-th gr-qcmath-phmath.MP

Paolo Aschieri , Christian Blohmann , Marija Dimitrijevic , Frank Meyer , Peter Schupp , Julius Wess This is my paper · ORCID
classification hep-thgr-qcmath-phmath.MP
keywords deformedactionalgebraconstructedcovariantdeformationmetricquantities
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A deformation of the algebra of diffeomorphisms is constructed for canonically deformed spaces with constant deformation parameter theta. The algebraic relations remain the same, whereas the comultiplication rule (Leibniz rule) is different from the undeformed one. Based on this deformed algebra a covariant tensor calculus is constructed and all the concepts like metric, covariant derivatives, curvature and torsion can be defined on the deformed space as well. The construction of these geometric quantities is presented in detail. This leads to an action invariant under the deformed diffeomorphism algebra and can be interpreted as a theta-deformed Einstein-Hilbert action. The metric or the vierbein field will be the dynamical variable as they are in the undeformed theory. The action and all relevant quantities are expanded up to second order in theta.

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Cited by 3 Pith papers

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  1. A new perspective on non-commutative deformations of field and gauge theories

    hep-th 2026-08 conditional novelty 7.0 of 10

    Star products built from active symmetry transformations give gauge-invariant non-commutative theories under a weakened unimodularity condition, with a planar equivalence theorem keeping internal Feynman structure undeformed.

  2. UV/IR mixing as an artifact of non-covariant quantisation

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    UV/IR mixing in noncommutative scalar field theories is shown to be an artifact of a non-covariant quantization choice rather than an intrinsic feature of noncommutativity.

  3. Bell nonlocality from twisted statistics

    quant-ph 2026-08 conditional novelty 5.0 of 10

    For a free scalar field on the Moyal plane, if the source couples to the twist-dressed field, the prepared two-particle state yields a maximal CHSH value S = 2 sqrt(1 + sin^2(chi/2)), exceeding 2 whenever the invarian...

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