%0 Journal Article
%T Wall-crossing, Rogers dilogarithm, and the QK/HK correspondence
%+ Laboratoire Charles Coulomb (L2C)
%+ Institute for Theoretical Physics [ETH Zürich] (ITP)
%+ Laboratoire de Physique Théorique et Hautes Energies (LPTHE)
%A Alexandrov, Sergey
%A Persson, Daniel
%A Pioline, Boris
%Z 67 pages, 1 figure
%< avec comité de lecture
%Z L2C:11-165
%@ 1126-6708
%J Journal of High Energy Physics
%I Springer
%V 2011
%N 12
%P 27
%8 2011-12-06
%D 2011
%Z 1110.0466
%R 10.1007/JHEP12(2011)027
%Z Physics [physics]/High Energy Physics - Theory [hep-th]
%Z Physics [physics]/Mathematical Physics [math-ph]
%Z Mathematics [math]/Algebraic Geometry [math.AG]
%Z Mathematics [math]/Differential Geometry [math.DG]
%Z Mathematics [math]/Mathematical Physics [math-ph]
%Z Mathematics [math]/Symplectic Geometry [math.SG]Journal articles
%X When formulated in twistor space, the D-instanton corrected hypermultiplet moduli space in N=2 string vacua and the Coulomb branch of rigid N=2 gauge theories on R^3 x S^1 are strikingly similar and, to a large extent, dictated by consistency with wall-crossing. We elucidate this similarity by showing that these two spaces are related under a general duality between, on one hand, quaternion-Kähler manifolds with a quaternionic isometry and, on the other hand, hyperkähler manifolds with a rotational isometry, further equipped with a hyperholomorphic circle bundle with a connection. We show that the transition functions of the hyperholomorphic circle bundle relevant for the hypermultiplet moduli space are given by the Rogers dilogarithm function, and that consistency across walls of marginal stability is ensured by the motivic wall-crossing formula of Kontsevich and Soibelman. We illustrate the construction on some simple examples of wall-crossing related to cluster algebras for rank 2 Dynkin quivers. In an appendix we also provide a detailed discussion on the general relation between wall-crossing and the theory of cluster algebras.
%G English
%2 https://hal.science/hal-00630135/document
%2 https://hal.science/hal-00630135/file/Alexandrov2011_Article_Wall-crossingRogersDilogarithm.pdf
%L hal-00630135
%U https://hal.science/hal-00630135
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%~ UPMC
%~ CNRS
%~ LPTHE
%~ L2C
%~ TDS-MACS
%~ UPMC_POLE_2
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%~ UNIV-MONTPELLIER
%~ SORBONNE-UNIVERSITE
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