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Published May 26, 2009 | public
Journal Article

Surface operators in Abelian gauge theory

Abstract

We consider arbitrary embeddings of surface operators in a pure, non-supersymmetric abelian gauge theory on spin (or non-spin) four-manifolds. For any surface operator with a priori simultaneously non-vanishing parameters, we explicitly show that the parameters transform naturally under an SL(2,Bbb Z) (or Γ_0(2)) duality of the theory. However, for non-trivially-embedded surface operators, S-duality holds only if the quantum parameter effectively vanishes, while the overall SL(2,Bbb Z) (or Γ_0(2)) duality holds up to a c-number at most, regardless. Via the formalism of duality walls, we furnish an alternative derivation of the transformation of parameters - found also to be consistent with a switch from Wilson to 't Hooft loop operators under S-duality. With any background embedding of surface operators, the partition function and the correlation functions of non-singular, gauge-invariant local operators on any curved four-manifold, are found to transform like modular forms under the respective duality groups.

Additional Information

© 2009 SISSA. Received 25 April 2009, accepted for publication 22 May 2009. Published 26 May 2009. This work is supported by the California Institute of Technology and the NUS-Overseas Postdoctoral Fellowship. E-print number: 0904.1744

Additional details

Created:
August 21, 2023
Modified:
October 19, 2023