Summing up Open String Instantons and N=1 String Amplitudes

Abstract

We compute the instanton expansions of the holomorphic couplings in the effective action of certain $\cx N=1$ supersymmetric four-dimensional open string vacua. These include the superpotential $W(\varphi )$, the gauge kinetic function $f(\varphi )$ and a series of other holomorphic couplings which are known to be related to amplitudes of topological open strings at higher world-sheet topologies. The results are in full agreement with the interpretation of the holomorphic couplings as counting functions of BPS domain walls. Similar techniques are used to compute genus one partition function for the closed topological string on Calabi--Yau 4-fold which gives rise to a theory with the same number of supercharges in two dimensions.

29 pages harvmac(b); v2: references added

References in corpus (19)

• Phases of $N=2$ Theories In Two Dimensions
• Superstrings and Topological Strings at Large N
• Mirror Symmetry, D-Branes and Counting Holomorphic Discs
• Disk Instantons, Mirror Symmetry and the Duality Web
• Open string instantons and superpotentials
• Solitons, Superpotentials and Calibrations
• BPS States of Exceptional Non-Critical Strings
• Mirror Manifolds in Higher Dimension
• Mirror Symmetry, N=1 Superpotentials and Tensionless Strings on Calabi-Yau Four-Folds
• Framed knots at large N
• On Link Invariants and Topological String Amplitudes
• Instanton sums and five-dimensional gauge theories
• Orientifolds, Mirror Symmetry and Superpotentials
• On N=1 Mirror Symmetry for Open Type II Strings
• Mirror Symmetry and a $G_2$ Flop
• $G_2$ Manifolds, Mirror Symmetry and Geometric Engineering
• Disc Instantons in Linear Sigma Models
• Enumerative geometry of stable maps with Lagrangian boundary conditions and multiple covers of the disc
• Localization of virtual classes

Cited by in corpus (16)

• Open string amplitudes and large order behavior in topological string theory
• Orientifolds of K3 and Calabi-Yau Manifolds with Intersecting D-branes
• Chern-Simons Theory and Topological Strings
• Enumerative geometry of Calabi-Yau 4-folds
• Superpotentials, A-infinity Relations and WDVV Equations for Open Topological Strings
• N=1 Special Geometry, Mixed Hodge Variations and Toric Geometry
• The D5-brane effective action and superpotential in N=1 compactifications
• Localization and Gluing of Topological Amplitudes
• D-branes and Normal Functions
• The Geometry of D-Brane Superpotentials
• Open Gromov-Witten Invariants of Toric Calabi-Yau 3-Folds
• Open Gromov-Witten invariants, mirror maps, and Seidel representations for toric manifolds
• Evidence for Tadpole Cancellation in the Topological String
• Orientifolds, Unoriented Instantons and Localization
• The Real Topological String on a local Calabi-Yau
• Special Geometry and Mirror Symmetry for Open String Backgrounds with N=1 Supersymmetry