Surface Operators in N=2 4d Gauge Theories

Abstract

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 will 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 will discuss a similar result about the tt* geometry of the surface operator. We will predict the existence and general features of a wall-crossing formula for BPS particles bound to the surface operator.

25 pages, 4 figures

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• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Loop and surface operators in N=2 gauge theory and Liouville modular geometry
• Gauge Theory Loop Operators and Liouville Theory
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