Journal of High Energy Physics

, 2016:179 | Cite as

Surface operators and separation of variables

  • Edward Frenkel
  • Sergei Gukov
  • Jörg Teschner
Open Access
Regular Article - Theoretical Physics


Alday, Gaiotto, and Tachikawa conjectured relations between certain 4d N = 2 supersymmetric field theories and 2d Liouville conformal field theory. We study generalizations of these relations to 4d theories with surface operators. For one type of surface operators the corresponding 2d theory is the WZW model, and for another type — the Liouville theory with insertions of extra degenerate fields. We show that these two 4d theories with surface operators exhibit an IR duality, which reflects the known relation (the so-called separation of variables) between the conformal blocks of the WZW model and the Liouville theory. Furthermore, we trace this IR duality to a brane creation construction relating systems of M5 and M2 branes in M-theory. Finally, we show that this duality may be expressed as an explicit relation between the generating functions for the changes of variables between natural sets of Darboux coordinates on the Hitchin moduli space.


Brane Dynamics in Gauge Theories Supersymmetric gauge theory 


Open Access

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.University of CaliforniaBerkeleyU.S.A.
  2. 2.California Institute of TechnologyPasadenaU.S.A.
  3. 3.Simons Center for Geometry and PhysicsStony BrookU.S.A.
  4. 4.DESY TheoryHamburgGermany

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