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Rigid surface operators. (English) Zbl 1203.81114

There are already familiar non-local operators in gauge theory, such as Wilson and ’t Hooft loop operators. By analogy, surface operators are supported on two-dimensional surfaces. In 2006 Gokov and Witten constructed half-BPS surface operators in \(N=4\) super Yang-Mills theory. It turns out, however, that those operators depend many parameters. In the present paper, the authors construct half-BPS surface operators that they call rigid as they do not depend on any free parameter. This is achieved via a simple construction. The four-dimensional spacetime is taken to be \(\mathbb{R}^4\) while the surface is simply \(\mathbb{R}^2\). Then an attempt is made to determine how these operators transform under duality, though this attempt is only partially successful, perhaps due to the simplicity (rigidity) of the construction. Some free parameters may change the situation. On the other hand, it becomes clear that the problem of describing all half-BPS surface operators in \(N=4\) super Yang-Mills theory is rather involved. Surface operators with reduced supersymmetry may be interesting, but harder to study. In addition to being ridid, the operators considered here are in a certain sense minimal or irreducible in that they do not have extra fields supported on the surface. Probably, ridid surface operators are conformally invariant, at least at the classical level. In the final section the authors describe string theoretic constructions of some of their ridid surface operators.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics
81T05 Axiomatic quantum field theory; operator algebras
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