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

Abstract

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 $\frac{1}{\eta }{\sum }_{n\in \mathbb{Z}}(-1{)}^n(6n+1{)}^k{q}^{(6n+1{)}^2/24}$ for $k=1,2,3,4$.

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

References in corpus (1)

• A Hiker's Guide to K3 - Aspects of N=(4,4) Superconformal Field Theory with central charge c=6