Superconformal Algebras and Mock Theta Functions
نویسنده
چکیده
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-Kähler 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.
منابع مشابه
Superconformal Algebras and Mock Theta Functions 2. Rademacher Expansion for K3 Surface
The elliptic genera of the K3 surfaces, both compact and non-compact cases, are studied by using the theory of mock theta functions. We decompose the elliptic genus in terms of the N = 4 superconformal characters at level-1, and present an exact formula for the coefficients of the massive (non-BPS) representations using Poincaré–Maass series.
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