Surface operators in \( \mathcal{N} = 2\) 4d gauge theories.

*(English)*Zbl 1397.81363Summary: \( \mathcal{N} = 2\) 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 |

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\textit{D. Gaiotto}, J. High Energy Phys. 2012, No. 11, Paper No. 90, 25 p. (2012; Zbl 1397.81363)

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