Superconformal Vortex Strings

TL;DR

This paper investigates the low-energy dynamics of vortex strings in Argyres-Douglas superconformal theories, revealing a connection between worldsheet models and four-dimensional superconformal theories.

Contribution

It demonstrates that the vortex string worldsheet is a deformation of the CP^N model flowing to a superconformal minimal model, establishing a correspondence between 2D and 4D superconformal theories.

Findings

Determined the scaling dimensions of chiral primary operators.

Found the dimensions of relevant perturbations agree in 2D and 4D.

Mapped the A-series of N=2 superconformal theories across dimensions.

Abstract

We study the low-energy dynamics of semi-classical vortex strings living above Argyres-Douglas superconformal field theories. The worldsheet theory of the string is shown to be a deformation of the CP^N model which flows in the infra-red to a superconformal minimal model. The scaling dimensions of chiral primary operators are determined and the dimensions of the associated relevant perturbations on the worldsheet and in the four dimensional bulk are found to agree. The vortex string thereby provides a map between the A-series of N=2 superconformal theories in two and four dimensions.