NDLI: D0–D6 States Counting and GW Invariants

Content Provider	Springer Nature Link
Author	Stoppa, Jacopo
Copyright Year	2012
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.
Ending Page	180
Page Count	32
Starting Page	149
File Format	PDF
ISSN	03779017
e-ISSN	15730530
Journal	Letters in Mathematical Physics
Issue Number	2
Volume Number	102
Language	English
Publisher	Springer Netherlands
Publisher Date	2012-04-15
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	wall-crossing Geometry Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants D0–D6 bound states Donaldson–Thomas invariants Gromov–Witten invariants Theoretical, Mathematical and Computational Physics Group Theory and Generalizations Statistical Physics, Dynamical Systems and Complexity Mirror symmetry
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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