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

Abstract

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.

Authors:
 [1];  [2];  [3]; ORCiD logo [4];  [5];  [5]
  1. Univ. of Amsterdam, Amsterdam (Netherlands)
  2. Emory Univ., Atlanta, GA (United States)
  3. Harvard Univ., Cambridge, MA (United States); McGill Univ., Montreal, QC (Canada)
  4. Univ. of Chicago, Chicago, IL (United States)
  5. Stanford Univ., Palo Alto, CA (United States). Stanford Inst. for Theoretical Physics
Publication Date:
Research Org.:
Harvard Univ., Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1505229
Grant/Contract Number:  
SC0007870
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 7; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; Black Holes in String Theory; Discrete Symmetries; M-Theory; Superstrings and Heterotic Strings

Citation Formats

Cheng, Miranda C. N., Duncan, John F. R., Harrison, Sarah M., Harvey, Jeffrey A., Kachru, Shamit, and Rayhaun, Brandon C. Attractive strings and five-branes, skew-holomorphic Jacobi forms and moonshine. United States: N. p., 2018. Web. doi:10.1007/jhep07(2018)130.
Cheng, Miranda C. N., Duncan, John F. R., Harrison, Sarah M., Harvey, Jeffrey A., Kachru, Shamit, & Rayhaun, Brandon C. Attractive strings and five-branes, skew-holomorphic Jacobi forms and moonshine. United States. doi:10.1007/jhep07(2018)130.
Cheng, Miranda C. N., Duncan, John F. R., Harrison, Sarah M., Harvey, Jeffrey A., Kachru, Shamit, and Rayhaun, Brandon C. Thu . "Attractive strings and five-branes, skew-holomorphic Jacobi forms and moonshine". United States. doi:10.1007/jhep07(2018)130. https://www.osti.gov/servlets/purl/1505229.
@article{osti_1505229,
title = {Attractive strings and five-branes, skew-holomorphic Jacobi forms and moonshine},
author = {Cheng, Miranda C. N. and Duncan, John F. R. and Harrison, Sarah M. and Harvey, Jeffrey A. and Kachru, Shamit and Rayhaun, Brandon C.},
abstractNote = {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.},
doi = {10.1007/jhep07(2018)130},
journal = {Journal of High Energy Physics (Online)},
number = 7,
volume = 2018,
place = {United States},
year = {2018},
month = {7}
}

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