A bstract Scaling black holes are solutions of supergravity with multiple hole singularities, which can be adiabatically connected to a single center solution. We develop techniques determine partition functions for such scaling holes, if each constituent carries non-vanishing magnetic charge corresponding D4-brane in string theory, or equivalently M5-brane M-theory. For three constituents, we ...

We discover a modular property of supersymmetric partition functions theories with R-symmetry in four dimensions. This is, sense, the generalization invariance function two-dimensional on torus i.e. elliptic genus. The question are manifolds homeomorphic to ones obtained by gluing solid tori. Such involves choice large diffeomorphism boundary torus, along gauge transformation for background fla...