2011/11/30 by Kazuhiro Sakai
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Amplitude #Anomaly (physics) #Geometric and Algebraic Topology #Geometry and complex manifolds #Holomorphic function #String (physics) #String theory #Surface (topology) #Topological string theory #Topology (electrical circuits) #hep-th #math.AG
paper · pdf · doi:10.1093/ptep/ptx027
35 pages, v2: several clarifications made, an equation and references added, v3: published version
openalex created_date 2016/06/24 · openalex publication_date 2017/02/20 · arxiv created 2017/04/02 · arxiv updated 2017/04/19 · openalex updated_date 2026/08/05
We study topological string amplitudes for the local half K3 surface. We develop a method of computing higher-genus amplitudes along the lines of the direct integration formalism, making full use of the Seiberg-Witten curve expressed in terms of modular forms and E8-invariant Jacobi forms. The Seiberg-Witten curve was constructed previously for the low-energy effective theory of the non-critical E-string theory in R4 x T2. We clarify how the amplitudes are written as polynomials in a finite number of generators expressed in terms of the Seiberg-Witten curve. We determine the coefficients of the polynomials by solving the holomorphic anomaly equation and the gap condition, and construct the amplitudes explicitly up to genus three. The results encompass topological string amplitudes for all local del Pezzo surfaces.