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Résumé |
The Dijkgraaf-Verlinde-Verlinde conjecture states that all 1/4 BPS states in four
dimensional string compactification with 16 supercharges have an (indexed)
partition function given by a genus 2 (Siegel) modular form of weight -10. From
this Siegel modular form, one can extract the (indexed) partition of those BPS
states/black holes that are immune to wall crossing effects, and these functions
are a one parameter family of mock Jacobi forms (of weight -10 and where the index
is parametrized by the T-duality invariant magnetic charge). These mock Jacobi
forms have been analyzed extensively and it is known how to recover both the one
parameter family of mock Jacobi forms and the Siegel modular form itself using the
Rademacher technique. However, the question of how the BPS black hole spectrum as
computed in supergravity sees this mock modularity remains an open question.
Progress towards this goal is reported in this talk, along with a comprehensive
introduction to the problem. |
