N=4 Characters in Gepner Models, Orbits and Elliptic Genera

Details N=4 Characters in Gepner Models, Orbits and Elliptic Genera N=4 Characters in Gepner Models, Orbits and Elliptic Genera

2003-04-11

arxiv.org/abs/hep-th/0304113v2

J.Math.Phys. 44 (2003) 5751-5792

Physics

High Energy Physics

High Energy Physics - Theory

39 pages; errors corrected in section 6, section 7 added (mixed Gepner models), ref added

Scientific paper

We review the properties of characters of the N=4 SCA in the context of a non-linear sigma model on $K3$, how they are used to span the orbits, and how the orbits produce topological invariants like the elliptic genus. We derive the same expression for the $K3$ elliptic genus using three different Gepner models ($1^6$, $2^4$ and $4^3$ theories), detailing the orbits and verifying that their coefficients $F_i$ are given by elementary modular functions. We also reveal the orbits for the $1^3 2^2$, $1^4 4$ and $1^2 4^2$ theories. We derive relations for cubes of theta functions and study the function $ {1\over\eta} \sum_{n\in \Z} (-1)^n (6n+1)^k q^{(6n+1)^2 /24} $ for $k=1,2,3,4$.

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