Index theorem boundary terms for gravitational instantons

Gibbons, G. W.; Pope, C.N.; Römer, Hartmann

doi:10.1016/0550-3213(79)90109-3

Cited by 49 publications

(80 citation statements)

References 15 publications

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“…Strictly speaking there seems to be no completely mathematically rigorous proof, in the manner of Ref. [28] that this 2-form exhausts the L 2 cohomology of Eguchi-Hanson but this conjecture is supported by index theorem calculations [29]. If ǫ = 0 and for k centres there is believed to be just a k − 1 dimensional space of anti-self-dual L 2 harmonic two-forms associated with the topology.…”

Section: Hyper-kähler Ale and Alf Spacesmentioning

confidence: 99%

Non-linear electrodynamics in curved backgrounds

Gibbons

Hashimoto

2000

J. High Energy Phys.

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We study non-linear electrodynamics in curved space from the viewpoint of dualities. After establishing the existence of a topological bound for self-dual configurations of Born-Infeld field in curved space, we check that the energy-momentum tensor vanishes. These properties are shown to hold for general duality-invariant non-linear electrodynamics. We give the dimensional reduction of Born-Infeld action to three dimensions in a general curved background admitting a Killing vector. The SO(2) duality symmetry becomes manifest but other symmetries present in flat space are broken, as is U-duality when one couples to gravity. We generalize our arguments on duality to the case of n U(1) gauge fields, and present a new Lagrangian possessing SO(n)×SO(2) elemag duality symmetry. Other properties of this model such as Legendre duality and enhancement of the symmetry by adding dilaton and axion, are studied. We extend our arguments to include a background b-field in the curved space, and give new examples including almost Kähler manifolds and Schwarzshild black holes with a b-field.

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Section: Hyper-kähler Ale and Alf Spacesmentioning

confidence: 99%

Non-linear electrodynamics in curved backgrounds

Gibbons

Hashimoto

2000

J. High Energy Phys.

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“…Standard formulae, which can be found in [33], lead for the Euler characteristic, χ E , and the Hirzebruch signature, τ H , to the results…”

Section: Index Theoremsmentioning

confidence: 99%

“…The so called G-index theorems allow the computation of the boundary corrections, ξ's, for which one finds [33] …”

Section: Index Theoremsmentioning

confidence: 99%

Explicit construction of Yang-Mills instantons on ALE spaces

et al. 1996

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We describe the explicit construction of Yang-Mills instantons on Asymptotically Locally Euclidean (ALE) spaces, following the work of Kronheimer and Nakajima. For multicenter ALE metrics, we determine the abelian instanton connections which are needed for the construction in the non-abelian case.We compute the partition function of Maxwell theories on ALE manifolds and comment on the issue of electromagnetic duality. We discuss the topological characterization of the instanton bundles as well as the identification of their moduli spaces. We generalize the 't Hooft ansatz to SU(2) instantons on ALE spaces and on other hyper-Kähler manifolds. Specializing to the Eguchi-Hanson gravitational background, we explicitly solve the ADHM equations for SU(2) gauge bundles with second

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“…For example, setting s equal to −2k, it is possible to safely equate a to zero and (20) gives the values of the expressions (18) and (19). I find,…”

Section: Zeta Functions and Heat-kernelsmentioning

confidence: 99%

“…The actual numbers for the various homogeneous (fixed point free) quotients of S 3 were computed by Gibbons et al, [18], who performed the group average by summing over the angles that define the elements. Something similar was done by Seade [19].…”

Section: The Eta Invariantmentioning

confidence: 99%

p-forms on d-spherical tessellations

Dowker¹

2007

Journal of Geometry and Physics

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Index theorem boundary terms for gravitational instantons

Cited by 49 publications

References 15 publications

Non-linear electrodynamics in curved backgrounds

Non-linear electrodynamics in curved backgrounds

Explicit construction of Yang-Mills instantons on ALE spaces

p-forms on d-spherical tessellations

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