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Wilson lines and UV sensitivity in magnetic compactifications. (English) Zbl 1380.81400
Summary: We investigate the ultraviolet (UV) behaviour of 6D $$N=1$$ supersymmetric effective (Abelian) gauge theories compactified on a two-torus ($$T_2$$) with magnetic flux. To this purpose we compute offshell the one-loop correction to the Wilson line state self-energy. The offshell calculation is actually necessary to capture the usual effective field theory expansion in powers of ($$\partial / \Lambda$$). Particular care is paid to the regularization of the (divergent) momentum integrals, which is relevant for identifying the corresponding counterterm(s). We find a counterterm which is a new higher dimensional effective operator of dimension $$d=6$$, that is enhanced for a larger compactification area (where the effective theory applies) and is consistent with the symmetries of the theory. Its consequences are briefly discussed and comparison is made with orbifold compactifications without flux.

##### MSC:
 81T60 Supersymmetric field theories in quantum mechanics 83E30 String and superstring theories in gravitational theory
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