Surface Operators

TL;DR

This paper reviews surface operators in N=2 supersymmetric gauge theories, exploring their relation to conformal field theory and the AGT correspondence, highlighting their mathematical properties and significance.

Contribution

It provides a comprehensive review of surface operators, their connection to degenerate fields in conformal field theory, and insights into their role in the AGT correspondence.

Findings

Surface operators are linked to degenerate fields in CFT.

Differential equations from degenerate fields help analyze correlation functions.

Understanding their origin in gauge theory may clarify the AGT correspondence.

Abstract

This is the seventh article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J.Teschner. It discusses an interesting class of observables localised on surfaces that attracts steadily growing attention. In the correspondence to conformal field theory some of these observables get related to a class of fields in two dimensions called degenerate fields. These fields satisfy differential equations that can be used to extract a lot of information on the correlation functions. Understanding the origin of these differential equations within gauge theory may help explaining the AGT-correspondence itself.