Skip to Main content Skip to Navigation
Journal articles

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

Abstract : 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.
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-00630135
Contributor : L2c Aigle <>
Submitted on : Monday, June 7, 2021 - 12:09:27 PM
Last modification on : Wednesday, June 9, 2021 - 8:59:01 AM

File

Alexandrov2011_Article_Wall-cr...
Publisher files allowed on an open archive

Licence


Distributed under a Creative Commons Attribution - NonCommercial 4.0 International License

Identifiers

Citation

Sergey Alexandrov, Daniel Persson, Boris Pioline. Wall-crossing, Rogers dilogarithm, and the QK/HK correspondence. Journal of High Energy Physics, Springer, 2011, 2011 (12), pp.27. ⟨10.1007/JHEP12(2011)027⟩. ⟨hal-00630135⟩

Share

Metrics

Record views

496