Surface Operators in N=2 4d Gauge Theories

TL;DR

This paper explores half BPS surface operators in N=2 4d gauge theories, revealing their rich geometric structures, relations to Seiberg-Witten theory, and potential wall-crossing phenomena affecting BPS states.

Contribution

It establishes a detailed connection between surface operator parameters, Seiberg-Witten geometry, and tt* geometry, introducing new insights into their interplay and wall-crossing behavior.

Findings

Relation between twisted couplings and Seiberg-Witten geometry

Analysis of tt* geometry for surface operators

Predictions of wall-crossing formulas for BPS states

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.