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

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If you have a question about this talk, please contact Mustapha Amrani.

Mathematics and Applications of Branes in String and M-theory

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 hyperkhler manifold. This construction relies on a general duality between 4n-dimensional quaternion-Khler and hyperkhler 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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