M-Theory and Topological Strings--I

Abstract

The $R^2{F}^{2g-2}$ terms of Type IIA strings on Calabi-Yau 3-folds, which are given by the corresponding topological string amplitudes (a worldsheet instanton sum for all genera), are shown to have a simple M-theory interpretation. In particular, a Schwinger one-loop computation in M-theory with wrapped M2 branes and Kaluza-Klein modes going around the loop reproduces the all genus string contributions from constant maps and worldsheet instanton corrections. In the simplest case of an isolated M2 brane with the topology of the sphere, we obtain the contributions of small worldsheet instantons (sphere ``bubblings'') which extends the results known or conjectured for low genera. Surprisingly, the 't Hooft expansion of large $N$ Chern-Simons theory on $S^3$ can also be used in a novel way to compute these gravitational terms at least in special cases.

14 pages

Cited by in corpus (35)

• The Refined Topological Vertex
• Curve counting via stable pairs in the derived category
• Stable pairs and BPS invariants
• Topological String Partition Functions as Polynomials
• Hodge integrals and degenerate contributions
• S-duality and Topological Strings
• Riemann-Hilbert problems from Donaldson-Thomas theory
• Finiteness and the Swampland
• Wall Crossing and M-theory
• Quantum moduli spaces from matrix models
• Bound state transformation walls
• Nonperturbative universal Chern-Simons theory
• Towards Classification of 5d SCFTs: Single Gauge Node
• Five-Dimensional Supersymmetric Yang-Mills Theories and Random Plane Partitions
• Confining Phase Superpotentials for SO/Sp Gauge Theories via Geometric Transition
• Disc Instantons in Linear Sigma Models
• Wall-crossing of D4-D2-D0 and flop of the conifold
• Quantum Curves, Resurgence and Exact WKB
• Analyticity of the Free Energy of a Closed 3-Manifold
• The Real Topological Vertex at Work
• Non-compact Topological Branes on Conifold
• Quantum K-Theory of Calabi-Yau Manifolds
• Uplifting the Iwasawa
• SO(N) Reformulated Link Invariants from Topological Strings
• Composite Representation Invariants and Unoriented Topological String Amplitudes
• Nekrasov's Partition Function and Refined Donaldson-Thomas Theory: the Rank One Case
• Counting embedded curves in symplectic 6-manifolds
• Calibrated Geometries and Non Perturbative Superpotentials in M-Theory
• Counting conifolds and Dijkgraaf-Vafa matrix models for three matrices
• Stable pair invariants of surfaces and Seiberg-Witten invariants
• Angular Momentum and Gravimagnetization of the $\mathcal{N}=2$ SYM vacuum
• Black Hole Partition Function using Hybrid Formalism of Superstrings
• Topological open string amplitudes on local toric del Pezzo surfaces via remodeling the B-model
• BPS Spectra, Barcodes and Walls
• Noncommutative resolutions and CICY quotients from a non-abelian GLSM