Superconformal algebras and mock theta functions

2008/12/31 by Tohru Eguchi, Kazuhiro Hikami
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Geometry and complex manifolds #hep-th #math-ph #math.MP

paper · pdf · doi:10.1088/1751-8113/42/30/304010

published as J.Phys.A42:304010,2009 · 28 pages

arxiv created 2009/03/02 · openalex publication_date 2009/07/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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 N=4 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-Kahler manifolds in higher dimensions. In particular we determine the elliptic genera in the case of complex 4 dimensions of the Hilbert scheme of points on K3 surfaces K^[2] and complex tori A^[[3]].

Citations

• The f(q) mock theta function conjecture and partition ranks
• The Final Problem : An Account of the Mock Theta Functions
• The definite integral ∫ _{- ∞} ^∞ \tfrace^{ax2 + bx} e^ax + dda and the analytic theory of numbersand the analytic theory of numbers
• On Modular Forms of Half Integral Weight