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

Cheng, Miranda C.  N.; Duncan, John F.  R.; Harrison, Sarah M.; Harvey, Jeffrey A.; Kachru, Shamit; Rayhaun, Brandon C.

doi:10.1007/jhep07(2018)130

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

Journal Article · Thu Jul 19 00:00:00 EDT 2018 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep07(2018)130· OSTI ID:1505229

Cheng, Miranda C. N. ^[1]; Duncan, John F. R. ^[2]; Harrison, Sarah M. ^[3];

^[4]; Kachru, Shamit ^[5]; Rayhaun, Brandon C. ^[5]

Univ. of Amsterdam, Amsterdam (Netherlands)
Emory Univ., Atlanta, GA (United States)
Harvard Univ., Cambridge, MA (United States); McGill Univ., Montreal, QC (Canada)
Univ. of Chicago, Chicago, IL (United States)
Stanford Univ., Palo Alto, CA (United States). Stanford Inst. for Theoretical Physics

We demonstrate 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 proposes 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.

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Research Organization:: Harvard Univ., Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0007870

OSTI ID:: 1505229

Journal Information:: Journal of High Energy Physics (Online), Vol. 2018, Issue 7; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 3 works

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Algebraic surfaces, four-folds and moonshine Lee, Kimyeong; Sarkis, Matthieu Journal of High Energy Physics, Vol. 2019, Issue 2 https://doi.org/10.1007/jhep02(2019)164	journal	February 2019
Vafa–Witten Theory and Iterated Integrals of Modular Forms Manschot, Jan Communications in Mathematical Physics, Vol. 371, Issue 2 https://doi.org/10.1007/s00220-019-03389-5	journal	March 2019
Vafa-Witten theory and iterated integrals of modular forms Manschot, Jan arXiv https://doi.org/10.48550/arxiv.1709.10098	text	January 2017

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

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