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Framed BPS states, moduli dynamics, and wall-crossing

  • Sungjay Lee
  • Piljin Yi
Article

Abstract

We formulate supersymmetric low energy dynamics for BPS dyons in strongly-coupled N = 2 Seiberg-Witten theories, and derive wall-crossing formulae thereof. For BPS states made up of a heavy core state and n probe (halo) dyons around it, we derive a reliable supersymmetric moduli dynamics with 3n bosonic coordinates and 4n fermionic superpartners. Attractive interactions are captured via a set of supersymmetric potential terms, whose detail depends only on the charges and the special Kähler data of the underlying N = 2 theories. The small parameters that control the approximation are not electric couplings but the mass ratio between the core and the probe, as well as the distance to the marginal stability wall where the central charges of the probe and of the core align. Quantizing the dynamics, we construct BPS bound states and derive the primitive and the semi-primitive wall-crossing formulae from the first principle. We speculate on applications to line operators and Darboux coordinates, and also about extension to supergravity setting.

Keywords

Extended Supersymmetry Solitons Monopoles and Instantons Duality in Gauge Field Theories String Duality 

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Copyright information

© SISSA, Trieste, Italy 2011

Authors and Affiliations

  1. 1.DAMTP, Centre for Mathematical SciencesUniversity of CambridgeCambridgeU.K.
  2. 2.School of PhysicsKorea Institute for Advanced StudySeoulKorea

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