Donaldson Invariants for Non-Simply Connected Manifolds

Mariño, Marcos; Moore, Gregory W.

doi:10.1007/s002200050611

Cited by 27 publications

(79 citation statements)

References 24 publications

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“…The final answer for F g in these cases will be given by a sum over the different blocks. The presence of α, β leads however to nontrivial modifications of the result, as it has been already noticed in various papers [48,27,47,42,40]. We will consider these modifications when we analyze the FHSV model.…”

Section: The F G Couplings In Heterotic String Theorymentioning

confidence: 81%

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Counting BPS States on the Enriques Calabi-Yau

Klemm

Mariño

2008

Commun. Math. Phys.

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128

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We study topological string amplitudes for the FHSV model using various techniques. This model has a type II realization involving a Calabi-Yau threefold with Enriques fibres, which we call the Enriques Calabi-Yau. By applying heterotic/type IIA duality, we compute the topological amplitudes in the fibre to all genera. It turns out that there are two different ways to do the computation that lead to topological couplings with different BPS content. One of them gives the standard D0-D2 counting amplitudes, and from the other one we obtain information about bound states of D0-D4-D2 branes on the Enriques fibre. We also study the model using mirror symmetry and the holomorphic anomaly equations. We verify in this way the heterotic results for the D0-D2 generating functional for low genera and find closed expressions for the topological amplitudes on the total space in terms of modular forms, and up to genus three. This model turns out to be much simpler than the generic B-model and might be exactly solvable.

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Section: The F G Couplings In Heterotic String Theorymentioning

confidence: 81%

“…More general cases can be also analyzed with the technique of lattice reduction, see [42,40] for examples.…”

Section: A Theta Functions and Modular Formsmentioning

confidence: 99%

Counting BPS States on the Enriques Calabi-Yau

Klemm

Mariño

2008

Commun. Math. Phys.

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128

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“…Equation (4.1) generalizes Witten's expression [15] for pure Yang-Mills and was obtained in section 11 of [2]. The extension of the N f = 0 Donaldson-Witten function to non-simply connected four-manifolds was begun in [2] [16], and completed in [17].…”

Section: The Donaldson-witten Function With Massive Hypermultipletsmentioning

confidence: 99%

Superconformal Invariance and the Geography¶of Four-Manifolds

Mariño¹,

Moore

Peradze³

1999

Communications in Mathematical Physics

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The correlation functions of supersymmetric gauge theories on a four-manifold X can sometimes be expressed in terms of topological invariants of X. We show how the existence of superconformal fixed points in the gauge theory can provide nontrivial information about four-manifold topology. In particular, in the example of gauge group SU (2) with one doublet hypermultiplet, we derive a theorem relating classical topological invariants such as the Euler character and signature to sum rules for Seiberg-Witten invariants. A short account of this paper can be found in [1].

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“…Notice that, as H 1 (Y, Z Z) ≃ Z Z, there are only two possible generators that differ in their sign. 5 To understand this dependence on the perturbation, it is useful to consider a four-dimensional version of this story, focusing again on the four manifold X = Y × S 1 , with b 1 (Y ) = 1. The structure of the cohomology ring of X is the following: We denote by S 2 a generator of H 2 (Y, Z Z) and by γ a generator…”

Section: 22b 1 (Y ) =mentioning

confidence: 99%