BPS states of curves in Calabi–Yau 3–folds

Bryan, Jim¹ ; Pandharipande, Rahul²

¹ Department of Mathematics, Tulane University, 6823 St Charles Ave, New Orleans, Louisiana 70118, USA
² Department of Mathematics, California Institute of Technology, Pasadena, California 91125, USA

Geometry & topology, Tome 5 (2001) no. 1, pp. 287-318.

Résumé

The Gopakumar–Vafa integrality conjecture is defined and studied for the local geometry of a super-rigid curve in a Calabi–Yau 3–fold. The integrality predicted in Gromov–Witten theory by the Gopakumar–Vafa BPS count is verified in a natural series of cases in this local geometry. The method involves Gromov–Witten computations, Möbius inversion, and a combinatorial analysis of the numbers of étale covers of a curve.

Détail

DOI : 10.2140/gt.2001.5.287

Keywords: Gromov–Witten invariants, BPS states, Calabi–Yau 3–folds

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