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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060

BPS states of curves in Calabi–Yau 3–folds

Jim Bryan and Rahul Pandharipande

Geometry & Topology 5 (2001) 287–318

DOI: 10.2140/gt.2001.5.287

arXiv: math.AG/0009025

Abstract

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.

Keywords

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

Mathematical Subject Classification

Primary: 14N35

Secondary: 81T30

References
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Publication

Received: 13 October 2000
Revised: 8 June 2002
Accepted: 20 March 2001
Published: 24 March 2001
Corrected: 8 June 2002
Proposed: Robion Kirby
Seconded: Yasha Eliashberg, Simon Donaldson

Authors
Jim Bryan
Department of Mathematics
Tulane University
6823 St Charles Ave
New Orleans
Louisiana 70118
USA
Rahul Pandharipande
Department of Mathematics
California Institute of Technology
Pasadena
California 91125
USA