Attractive strings and five-branes, skew-holomorphic Jacobi forms and moonshine

• Published in: The journal of high energy physics Vol. 2018; no. 7; pp. 1 - 29
• Main Authors: Cheng, Miranda C. N., Duncan, John F. R., Harrison, Sarah M., Harvey, Jeffrey A., Kachru, Shamit, Rayhaun, Brandon C.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2018; Springer Nature B.V; Springer Berlin; SpringerOpen
• Subjects: ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; Black Holes in String Theory; Branes; Classical and Quantum Gravitation; Discrete Symmetries; Elementary Particles; High energy physics; M-Theory; Mathematical analysis; Physics; Physics and Astronomy; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Strings; Superstrings and Heterotic Strings; Black Holes in String Theory; Discrete Symmetries; Superstrings and Heterotic Strings; M-Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP07(2018)130

A bstract We show that certain BPS counting functions for both fundamental strings and strings arising from fivebranes wrapping divisors in Calabi-Yau threefolds naturally give rise to skew-holomorphic Jacobi forms at rational and attractor points in the moduli space of string compactifications. For M5-branes wrapping divisors these are forms of weight negative one, and in the case of multiple M5-branes skew-holomorphic mock Jacobi forms arise. We further find that in simple examples these forms are related to skew-holomorphic (mock) Jacobi forms of weight two that play starring roles in moonshine. We discuss examples involving M5-branes on the complex projective plane, del Pezzo surfaces of degree one, and half-K3 surfaces. For del Pezzo surfaces of degree one and certain half-K3 surfaces we find a corresponding graded (virtual) module for the degree twelve Mathieu group. This suggests a more extensive relationship between Mathieu groups and complex surfaces, and a broader role for M5-branes in the theory of Jacobi forms and moonshine.