Topological Strings, Instantons and Asymptotic Forms of Gopakumar-Vafa Invariants

Abstract

We calculate the topological string amplitudes of Calabi-Yau toric threefolds corresponding to 4D, N=2, SU(2) gauge theory with N_f=0,1,2,3,4 fundamental hypermultiplets by using the method of the geometric transition and show that they reproduce Nekrasov's formulas for instanton counting. We also determine the asymptotic forms of the Gopakumar-Vafa invariants of the Calabi-Yau threefolds including those at higher genera from instanton amplitudes of the gauge theory.

arXiv comment25 pages, 5 figures; (v2) eq.(10) corrected

References in corpus (3)

• Geometric Engineering of Quantum Field Theories
• Seiberg-Witten prepotential from instanton counting
• Geometric Engineering of Seiberg-Witten Theories with Massive Hypermultiplets

Cited by in corpus (7)

• Chern-Simons Theory and Topological Strings
• Parabolic refined invariants and Macdonald polynomials
• Geometric engineering of (framed) BPS states
• Wallcrossing and Cohomology of The Moduli Space of Hitchin Pairs
• Topological String Partition Functions as Equivariant Indices
• BPS states and the P=W conjecture
• Dimensional Reduction of Seiberg-Witten Monopole Equations, N=2 Noncommutative Supersymmetric Field Theories and Young Diagrams