Surface Operators in Abelian Gauge Theory

Abstract

We consider arbitrary embeddings of surface operators in a pure, non-supersymmetric abelian gauge theory on spin (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, Z) (or a congruence subgroup thereof) duality of the theory. However, for non-trivially-embedded surface operators, exact S-duality holds only if the quantum parameter effectively vanishes, while the overall SL(2, Z) (or a congruence subgroup thereof) 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.

30 pages. Minor refinement

References in corpus (5)

• Gauge Theory, Ramification, And The Geometric Langlands Program
• Bubbling Surface Operators And S-Duality
• Instanton counting via affine Lie algebras I: Equivariant J-functions of (affine) flag manifolds and Whittaker vectors
• Holographic Gauge Theories in Background Fields and Surface Operators
• Holography of BPS surface operators

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