Non-perturbative effects and wall-crossing from topological strings

Abstract

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.

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

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Cited by in corpus (16)

• Instantons and infinite distances
• Instanton Corrections and Emergent Strings
• F-theory at order ${\alpha }^{\prime 3}$
• On α' corrections in N=1 F-theory compactifications
• BPS Wall Crossing and Topological Strings
• Infinite Distances and the Axion Weak Gravity Conjecture
• Emergence of Species Scale Black Hole Horizons
• On the computation of non-perturbative effective potentials in the string theory landscape -- IIB/F-theory perspective
• Wall-crossing of D4-D2-D0 and flop of the conifold
• Branes and instantons intersecting at angles
• D-instanton and polyinstanton effects from type I' D0-brane loops
• Multiple D4-D2-D0 on the Conifold and Wall-crossing with the Flop
• On quantum corrected Kähler potentials in F-theory
• Heterotic-Type II duality in the hypermultiplet sector
• Evidence for Duality of Conifold from Fundamental String
• Topics in Open Topological Strings