Non-perturbative effects and wall-crossing from topological strings

Details Non-perturbative effects and wall-crossing from topological strings Non-perturbative effects and wall-crossing from topological strings

2009-04-07

arxiv.org/abs/0904.1133v2

JHEP 0911:025,2009

Physics

High Energy Physics

High Energy Physics - Theory

44 pages, 5 figures. Major revisions, new results added, previous results unchanged, refs added

Scientific paper

10.1088/1126-6708/2009/11/025

We argue that the Gopakumar-Vafa interpretation of the topological string partition function can be used to compute and resum certain non-perturbative brane instanton effects of type II CY compactifications. In particular the topological string A-model encodes the non-perturbative corrections to the hypermultiplet moduli space metric from general D1/D(-1)-brane instantons in 4d N=2 IIB models. We also discuss the reduction to 4d N=1 by fluxes and/or orientifolds and/or D-branes, and the prospects to resum brane instanton contributions to non-perturbative superpotentials. We argue that the connection between non-perturbative effects and the topological string underlies the continuity of non-perturbative effects across lines of BPS stability. We also confirm this statement in mirror B-model matrix model examples, relating matrix model instantons to non-perturbative D-brane instantons. The computation of non-perturbative effects from the topological string requires a 3d circle compactification and T-duality, relating effects from particles and instantons, reminiscent of that involved in the physical derivation of the Kontsevich-Soibelmann wall-crossing formula.

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