We describe a correspondence between the Donaldson–Thomas invariants enumerating D0–D6 bound states on a Calabi–Yau 3-fold and certain Gromov–Witten invariants counting rational curves in a family of blowups of weighted projective planes. This is a variation on a correspondence found by Gross–Pandharipande, with D0–D6 bound states replacing representations of generalised Kronecker quivers. We build on a small part of the theories developed by Joyce–Song and Kontsevich–Soibelman for wall-crossing formulae and by Gross–Pandharipande–Siebert for factorisations in the tropical vertex group. Along the way we write down an explicit formula for the BPS state counts which arise up to rank 3 and prove their integrality. We also compare with previous “noncommutative DT invariants” computations in the physics literature.

D0-D6 states counting and GW invariants / Stoppa, Jacopo. - In: LETTERS IN MATHEMATICAL PHYSICS. - ISSN 0377-9017. - 102:2(2012), pp. 149-180. [10.1007/s11005-012-0560-y]

D0-D6 states counting and GW invariants

Stoppa, Jacopo
2012-01-01

Abstract

We describe a correspondence between the Donaldson–Thomas invariants enumerating D0–D6 bound states on a Calabi–Yau 3-fold and certain Gromov–Witten invariants counting rational curves in a family of blowups of weighted projective planes. This is a variation on a correspondence found by Gross–Pandharipande, with D0–D6 bound states replacing representations of generalised Kronecker quivers. We build on a small part of the theories developed by Joyce–Song and Kontsevich–Soibelman for wall-crossing formulae and by Gross–Pandharipande–Siebert for factorisations in the tropical vertex group. Along the way we write down an explicit formula for the BPS state counts which arise up to rank 3 and prove their integrality. We also compare with previous “noncommutative DT invariants” computations in the physics literature.
2012
102
2
149
180
https://link.springer.com/article/10.1007%2Fs11005-012-0560-y
https://arxiv.org/abs/0912.2923
Stoppa, Jacopo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/14083
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