Moduli of half conformally flat structures

Itoh, Mitsuhiro

doi:10.1007/bf01445130

Cited by 18 publications

(21 citation statements)

References 35 publications

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“…This deformation theory already appeared implicitly in Floer's work [8] and is spelled out in generality by Kotschick and King [15], [11]. This deformation theory already appeared implicitly in Floer's work [8] and is spelled out in generality by Kotschick and King [15], [11].…”

Section: Introductionmentioning

confidence: 94%

Equivariant connected sums of compact self-dual manifolds

Pedersen¹,

Poon

1995

Math. Ann.

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Section: Introductionmentioning

confidence: 94%

Equivariant connected sums of compact self-dual manifolds

Pedersen¹,

Poon

1995

Math. Ann.

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“…the Weyl tensor is anti-self-dual (e.g. see [51]). 27 We thank S. Gukov for discussing this idea with us.…”

Section: Infraredmentioning

confidence: 99%

Kähler uniformization from holographic renormalization group flows of M5-branes

Fluder

2018

J. High Energ. Phys.

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In this paper, we initiate the study of holographic renormalization group flows for the metric of four-manifolds. In particular, we derive a set of equations which govern the evolution of a generic Kähler four-manifold along the renormalization group flow in seven-dimensional gauged supergravity. The physical eleven-dimensional M-theory setup is given by a stack of M5-branes wrapping a calibrated Kähler four-cycle inside a CalabiYau threefold. By topologically twisting the theory in the ultraviolet, we may choose an arbitrary Kähler metric on the four-cycle as an asymptotic boundary condition. We find that at the infrared fixed point, we reach a Kähler-Einstein metric, which can be interpreted as an indication of "uniformizing" behavior of the flow.

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“…We briefly recall some details of moduli space theory [Ito93,KK92] (these references deal with the case of smooth manifolds, but the proofs are easily generalized to the setting of orbifolds). Given an anti-self-dual metric g on a compact orbifold, there is a map Ψ : H 1 → H 2 , called the Kuranishi map which is equivariant with respect to the action of H 0 , and the moduli space of anti-self-dual conformal structures near g is locally isomorphic to Ψ −1 (0)/H 0 .…”

Section: Introductionmentioning

confidence: 99%

An Index Theorem on Anti-Self-Dual Orbifolds

Viaclovsky

2012

International Mathematics Research Notices

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Abstract. An index theorem for the anti-self-dual deformation complex on antiself-dual orbifolds with singularities conjugate to ADE-type is proved. In 1988, Claude Lebrun gave examples of scalar-flat Kähler ALE metrics with negative mass, on the total space of the bundle O(−n) over S 2 . A corollary of this index theorem is that the moduli space of anti-self-dual ALE metrics near each of these metrics has dimension at least 4n − 12, and thus for n ≥ 4 the LeBrun metrics admit a plethora of non-trivial anti-self-dual deformations.

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Moduli of half conformally flat structures

Cited by 18 publications

References 35 publications

Equivariant connected sums of compact self-dual manifolds

Equivariant connected sums of compact self-dual manifolds

Kähler uniformization from holographic renormalization group flows of M5-branes

An Index Theorem on Anti-Self-Dual Orbifolds

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