2006
DOI: 10.1016/j.nuclphysb.2006.04.019
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Geometry of manifolds with area metric: Multi-metric backgrounds

Abstract: We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings, and is considerably more general than Lorentzian geometry. Our construction of geometrically relevant objects, such as an area metric compatible connection and derived tensors, makes essential use of a decomposition theorem due to Gilkey, whereby we generate the area metric fr… Show more

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Cited by 29 publications
(64 citation statements)
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“…Part One (sections [1][2][3][4][5][6][7] develops the foundations of area metric geometry in detail. Its practical results, however, are concisely summarized in the first section of Part Two (sections [8][9][10][11][12][13][14] where the area metric version of Einstein-Hilbert gravity is formulated in general, and then applied to area metric cosmology. A more detailed outline of the individual sections of the paper is given at the beginning of each of the two parts.…”
Section: Invitationmentioning
confidence: 99%
“…Part One (sections [1][2][3][4][5][6][7] develops the foundations of area metric geometry in detail. Its practical results, however, are concisely summarized in the first section of Part Two (sections [8][9][10][11][12][13][14] where the area metric version of Einstein-Hilbert gravity is formulated in general, and then applied to area metric cosmology. A more detailed outline of the individual sections of the paper is given at the beginning of each of the two parts.…”
Section: Invitationmentioning
confidence: 99%
“…The construction of differential operators relevant for the geometry of areas in this paper is completely canonical: the area metric is treated as a fundamental structure on the manifold, which contrasts our recent work in [9], where area metric geometry was discussed as a multi-metric geometry by employing a particular Gilkey decomposition [10,11] of the area metric. The identification of canonical differential geometric structures in the present paper sets the stage for the search for area geometric invariants which, in the light of our findings, promise to be of relevance for the description of gravity on D-branes [12 -15].…”
Section: Jhep02(2006)059mentioning
confidence: 99%
“…where ε is the totally antisymmetric density, and the determinant is calculated for G : 16) which is equivalent to ∇ X ω = 0 as shown in [9]. This in turn implies that the simplicity condition Ω∧Ω = 0 (for Ω to be an area in A 2 T M ), which may be written ω(Ω, Ω, * , .…”
Section: Jhep02(2006)059mentioning
confidence: 99%
“…Such a generalized spacetime geometry would have to be sufficiently general to capture various of the anomalies currently escaping explanation, while at the same time providing feasible spacetime backgrounds for particle physics. Area metric manifolds [13] present a promising candidate for a refinement of Lorentzian geometry addressing these issues. In particular, one can write down a refinement of the Einstein-Hilbert action, such that the gravitational field is encoded in an area metric.…”
Section: Introductionmentioning
confidence: 99%