S-duality transformation of SYM theory at the operator level
arXiv:1903.01199
Abstract
We consider the S-duality transformation of gauge invariant operators and states in SYM theory. The transformation is realized through an operator which is the canonical transformation in loop space with the gauge invariant electric and the magnetic flux operators composing the canonical variables. Based on , S-duals for all of the physical operators and states can be defined. The criterion for the theory to be S-duality invariant is that the superconformal charges and their S-duals differ by a phase. The verification can be done by checking the S transformation for supersymmetry and special supersymmetry variations of the loop operators. The fact that supercharges preserved by BPS Wilson operators and the S-dual BPS 't Hooft operators differ by a chiral rotation could in some sense serve as a proof.
arXiv comment25 pages; v2: 29 pages, reference added; v3: restructured, clarifications added
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