The paper traces the global-structure ambiguity of 6d (2,0) theories to non-commuting RR flux boundary conditions in IIB on C^2/Γ, reproducing the known classification of 4d N=4 theories and adding new results on duality defects and Hecke transforms.
Line operators from M-branes on compact Riemann surfaces
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abstract
In this paper, we determine the charge lattice of mutually local Wilson and 't Hooft line operators for class S theories living on M5-branes wrapped on compact Riemann surfaces. The main ingredients of our analysis are the fundamental group of the N-cover of the Riemann surface, and a quantum constraint on the six-dimensional theory. This latter plays a central role in excluding some of the possible lattices and imposing consistency conditions on the charges. This construction gives a geometric explanation for the mutual locality among the lines, fixing their charge lattice and the structure of the four-dimensional gauge group.
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IIB flux non-commutativity and the global structure of field theories
The paper traces the global-structure ambiguity of 6d (2,0) theories to non-commuting RR flux boundary conditions in IIB on C^2/Γ, reproducing the known classification of 4d N=4 theories and adding new results on duality defects and Hecke transforms.