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Wall-crossing, dilogarithm identities and the QK/HK correspondence

Friday 13th January 2012 - 14:00 to 15:00
INI Seminar Room 1
I will explain how the wall-crossing behaviour of D-brane instantons in type II Calabi-Yau compactifications is captured by a certain hyperholomorphic line bundle over a hyperkähler manifold. This construction relies on a general duality between 4n-dimensional quaternion-Kähler and hyperkähler spaces with certain continuous isometries. The continuity of the moduli space metric across walls of marginal stability is encoded in non-trivial identities for the Rogers dilogarithm, which are shown to be a consequence of the motivic Kontsevich-Soibelman wall-crossing formula. Finally, I will offer some speculations on how the construction is modified in the presence of NS5-brane effects.
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons