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Résumé |
In type II strings compactified on a Calabi-Yau threefold, BPS black hole microstates are
counted by generalized Donaldson-Thomas invariants. The latter exhibit well-understood but
complicated wall-crossing phenomena. Using constraints from string dualities, I will argue that
the generating function of DT invariants supported on a 4-cycle must be in general be a mock
modular form of higher depth, a concept which I will explain and illustrate. This generating
function is closely related to the elliptic genus of the Maldacena-Strominger-Witten
superconformal field theory on a wrapped M5-brane, and to the partition function of
topologically twisted N=4 Yang-Mills theory on a wrapped D4-brane.
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