D0-D6 States Counting and GW Invariants

被引:7
作者
Stoppa, Jacopo [1 ]
机构
[1] Univ Cambridge, Dept Pure Math & Math Stat, Cambridge CB3 0WB, England
关键词
D0-D6 bound states; Donaldson-Thomas invariants; Gromov-Witten invariants; wall-crossing; DONALDSON-THOMAS INVARIANTS; THREEFOLDS;
D O I
10.1007/s11005-012-0560-y
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
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.
引用
收藏
页码:149 / 180
页数:32
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