Refined stable pair invariants for E-, M- and [p, q]-strings

2013/08/02 by Min-xin Huang, Albrecht Klemm, Maximilian Poretschkin · 3 citations
Mathematics · Physics and Astronomy · #Anomaly (physics) #Black Holes and Theoretical Physics #Gauge theory #Geometry #Gravitational singularity #Holomorphic function #Instanton #Mathematical physics #Mathematics #Mirror symmetry #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Supersymmetric gauge theory #Symmetry (geometry) #Theoretical physics #hep-th

paper · pdf · doi:10.1007/jhep11(2013)112

120 pages, 21 figures

arxiv created 2013/08/02 · openalex publication_date 2013/11/01 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We use mirror symmetry, the refined holomorphic anomaly equation and modularity properties of elliptic singularities to calculate the refined BPS invariants of stable pairs on non-compact Calabi-Yau manifolds, based on del Pezzo surfaces and elliptic surfaces, in particular the half K3. The BPS numbers contribute naturally to the five-dimensional N=1 supersymmetric index of M-theory, but they can be also interpreted in terms of the superconformal index in six dimensions and upon dimensional reduction the generating functions count N=2 Seiberg-Witten gauge theory instantons in four dimensions. Using the M/F-theory uplift the additional information encoded in the spin content can be used in an essential way to obtain information about BPS states in physical systems associated to small instantons, tensionless strings, gauge symmetry enhancement in F-theory by [p,q]-strings as well as M-strings.

Citations

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Cited by

• Peacock patterns and new integer invariants in topological string theory
• The U-plane of rank-one 4d N=2 KK theories
• BPS relations from spectral problems and blowup equations