### Abstract

It is known that characters of BPS representations of extended superconformal algebras do not have good modular properties due to extra singular vectors coming from the BPS condition. In order to improve their modular properties we apply the method of Zwegers which has recently been developed to analyze modular properties of mock theta functions. We consider the case of the superconformal algebra at general levels and obtain the decomposition of characters of BPS representations into a sum of simple Jacobi forms and an infinite series of non-BPS representations. We apply our method to study elliptic genera of hyper-Kähler manifolds in higher dimensions. In particular, we determine the elliptic genera in the case of complex four dimensions of the Hilbert scheme of points on K3 surfaces K^{[2]} and complex tori A^{[[3]]}.

Original language | English |
---|---|

Article number | 304010 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 42 |

Issue number | 30 |

DOIs | |

Publication status | Published - Nov 23 2009 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*42*(30), [304010]. https://doi.org/10.1088/1751-8113/42/30/304010

**Superconformal algebras and mock theta functions.** / Eguchi, Tohru; Hikami, Kazuhiro.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 42, no. 30, 304010. https://doi.org/10.1088/1751-8113/42/30/304010

}

TY - JOUR

T1 - Superconformal algebras and mock theta functions

AU - Eguchi, Tohru

AU - Hikami, Kazuhiro

PY - 2009/11/23

Y1 - 2009/11/23

N2 - It is known that characters of BPS representations of extended superconformal algebras do not have good modular properties due to extra singular vectors coming from the BPS condition. In order to improve their modular properties we apply the method of Zwegers which has recently been developed to analyze modular properties of mock theta functions. We consider the case of the superconformal algebra at general levels and obtain the decomposition of characters of BPS representations into a sum of simple Jacobi forms and an infinite series of non-BPS representations. We apply our method to study elliptic genera of hyper-Kähler manifolds in higher dimensions. In particular, we determine the elliptic genera in the case of complex four dimensions of the Hilbert scheme of points on K3 surfaces K[2] and complex tori A[[3]].

AB - It is known that characters of BPS representations of extended superconformal algebras do not have good modular properties due to extra singular vectors coming from the BPS condition. In order to improve their modular properties we apply the method of Zwegers which has recently been developed to analyze modular properties of mock theta functions. We consider the case of the superconformal algebra at general levels and obtain the decomposition of characters of BPS representations into a sum of simple Jacobi forms and an infinite series of non-BPS representations. We apply our method to study elliptic genera of hyper-Kähler manifolds in higher dimensions. In particular, we determine the elliptic genera in the case of complex four dimensions of the Hilbert scheme of points on K3 surfaces K[2] and complex tori A[[3]].

UR - http://www.scopus.com/inward/record.url?scp=70449659267&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70449659267&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/42/30/304010

DO - 10.1088/1751-8113/42/30/304010

M3 - Article

AN - SCOPUS:70449659267

VL - 42

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 30

M1 - 304010

ER -