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

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:

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

Publication Date:: 2018-07-19

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

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

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.

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                    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.  https://doi.org/10.1007/jhep07(2018)130

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                    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.  https://doi.org/10.1007/jhep07(2018)130.  https://www.osti.gov/servlets/purl/1505229.

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@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}

}

Copy to clipboard

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Works referencing / citing this record:

Algebraic surfaces, four-folds and moonshine
journal, February 2019

Lee, Kimyeong; Sarkis, Matthieu
Journal of High Energy Physics, Vol. 2019, Issue 2
DOI: 10.1007/jhep02(2019)164

Vafa–Witten Theory and Iterated Integrals of Modular Forms
journal, March 2019

Manschot, Jan
Communications in Mathematical Physics, Vol. 371, Issue 2
DOI: 10.1007/s00220-019-03389-5

Vafa-Witten theory and iterated integrals of modular forms
text, January 2017

Manschot, Jan
arXiv
DOI: 10.48550/arxiv.1709.10098

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Similar Records

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

Abstract

Citation Formats

Heegner cycles, modular forms and jacobi forms journal, January 1991

Naturality in conformal field theory journal, January 1989

Calabi–Yau Black Holes and (0,4) Sigma Models journal, February 2000

The Betti numbers of the Hilbert scheme of points on a smooth projective surface journal, March 1990

Split states, entropy enigmas, holes and halos journal, November 2011

Integral Symmetric Bilinear Forms and some of Their Applications journal, February 1980

E-strings and N = 4 topological Yang-Mills theories journal, September 1998

Explicit formulas for the Fourier coefficients of Jacobi and elliptic modular forms journal, December 1990

The M5-brane elliptic genus: modularity and BPS states journal, August 2007

The Betti numbers of the moduli space of stable sheaves of rank 2 on a ruled surface journal, May 1995

Traces of singular moduli and moonshine for the Thompson group journal, January 2016

A modern fareytail journal, January 2010

A strong coupling test of S-duality journal, December 1994

Jacobi forms and a certain space of modular forms journal, February 1988

Finite simple groups which projectively embed in an exceptional Lie group are classified! journal, January 1999

Wall-Crossing Holomorphic Anomaly and Mock Modularity of Multiple M5-Branes journal, August 2015

A Farey tail for attractor black holes journal, November 2006

Notes on the K3 Surface and the Mathieu Group M 24 journal, March 2011

Umbral moonshine and the Niemeier lattices journal, June 2014

Nonrenormalization of the superstring tension journal, July 1989

Weight one Jacobi forms and umbral moonshine journal, February 2018

Black holes and Hurwitz class numbers journal, October 2017

Black hole entropy in M-Theory journal, December 1997

Black Holes and Hurwitz Class Numbers text, January 2017

The M5-Brane Elliptic Genus: Modularity and BPS States text, January 2006

A Farey Tail for Attractor Black Holes text, January 2006

Split States, Entropy Enigmas, Holes and Halos text, January 2007

Algebraic surfaces, four-folds and moonshine journal, February 2019

Vafa–Witten Theory and Iterated Integrals of Modular Forms journal, March 2019

Vafa-Witten theory and iterated integrals of modular forms text, January 2017

Heegner cycles, modular forms and jacobi forms
journal, January 1991

Naturality in conformal field theory
journal, January 1989

Calabi–Yau Black Holes and (0,4) Sigma Models
journal, February 2000

The Betti numbers of the Hilbert scheme of points on a smooth projective surface
journal, March 1990

Split states, entropy enigmas, holes and halos
journal, November 2011

Integral Symmetric Bilinear Forms and some of Their Applications
journal, February 1980

E-strings and N = 4 topological Yang-Mills theories
journal, September 1998

Explicit formulas for the Fourier coefficients of Jacobi and elliptic modular forms
journal, December 1990

The M5-brane elliptic genus: modularity and BPS states
journal, August 2007

The Betti numbers of the moduli space of stable sheaves of rank 2 on a ruled surface
journal, May 1995

Traces of singular moduli and moonshine for the Thompson group
journal, January 2016

A modern fareytail
journal, January 2010

A strong coupling test of S-duality
journal, December 1994

Jacobi forms and a certain space of modular forms
journal, February 1988

Finite simple groups which projectively embed in an exceptional Lie group are classified!
journal, January 1999

Wall-Crossing Holomorphic Anomaly and Mock Modularity of Multiple M5-Branes
journal, August 2015

A Farey tail for attractor black holes
journal, November 2006

Notes on the K3 Surface and the Mathieu Group M ₂₄
journal, March 2011

Umbral moonshine and the Niemeier lattices
journal, June 2014

Nonrenormalization of the superstring tension
journal, July 1989

Weight one Jacobi forms and umbral moonshine
journal, February 2018

Black holes and Hurwitz class numbers
journal, October 2017

Black hole entropy in M-Theory
journal, December 1997

Black Holes and Hurwitz Class Numbers
text, January 2017

The M5-Brane Elliptic Genus: Modularity and BPS States
text, January 2006

A Farey Tail for Attractor Black Holes
text, January 2006

Split States, Entropy Enigmas, Holes and Halos
text, January 2007

Algebraic surfaces, four-folds and moonshine
journal, February 2019

Vafa–Witten Theory and Iterated Integrals of Modular Forms
journal, March 2019

Vafa-Witten theory and iterated integrals of modular forms
text, January 2017