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Surface operators in $$\mathcal{N} = 2$$ 4d gauge theories. (English) Zbl 1397.81363
Summary: $$\mathcal{N} = 2$$ four dimensional gauge theories admit interesting half BPS surface operators preserving a (2, 2) two dimensional SUSY algebra. Typical examples are (2, 2) 2d sigma models with a flavor symmetry which is coupled to the 4d gauge fields. Interesting features of such 2d sigma models, such as (twisted) chiral rings, and the $$tt^*$$ geometry, can be carried over to the surface operators, and are affected in surprising ways by the coupling to 4d degrees of freedom. We describe in detail a relation between the parameter space of twisted couplings of the surface operator and the Seiberg-Witten geometry of the bulk theory. We discuss a similar result about the $$tt^*$$ geometry of the surface operator. We predict the existence and general features of a wall-crossing formula for BPS particles bound to the surface operator.

##### MSC:
 81T60 Supersymmetric field theories in quantum mechanics
##### Keywords:
supersymmetry and duality; extended supersymmetry
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##### References:
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