2003/10/31 by Tohru Eguchi, Hiroaki Kanno · 108 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Gauge (firearms) #Gauge theory #Holomorphic function #Non-critical string theory #Quantum Chromodynamics and Particle Interactions #Quantum and Classical Electrodynamics #String (physics) #String field theory #Topological quantum field theory #Topological string theory #Topology (electrical circuits) #hep-th
paper · pdf · doi:10.1088/1126-6708/2003/12/006
published in Journal of High Energy Physics 2003(12), 006 (Springer Nature) · 38 pages, 4 figures, (v2) References added, Appendices expanded, (v3) Typos corrected, References added
openalex publication_date 2003/12/03 · arxiv created 2003/12/17 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We apply the method of geometric transition and compute all genus topological closed string amplitudes compactified on local \bf F0 by making use of the Chern-Simons gauge theory. We find an exact agreement of the results of our computation with the formula proposed recently by Nekrasov for \cal N=2 SU(2) gauge theory with two parameters βand ℏ. βis related to the size of the fiber of \bf F0 and ℏ corresponds to the string coupling constant. Thus Nekrasov's formula encodes all the information of topological string amplitudes on local \bf F0 including the number of holomorphic curves at arbitrary genus. By taking suitable limits βand/or ℏ → 0 one recovers the four-dimensional Seiberg-Witten theory and also its coupling to external graviphoton fields. We also compute topological string amplitude for the local 2nd del Pezzo surface and check the consistency with Nekrasov's formula of SU(2) gauge theory with a matter field in the vector representation.