Argyres-Douglas Theories, S^1 Reductions, and Topological Symmetries

TL;DR

This paper explores the S^1 reduction of Argyres-Douglas theories, revealing how topological symmetries and R symmetry mixing influence the resulting theories and their operator dimensions.

Contribution

It provides a detailed analysis of the S^1 reduction of AD theories, identifying R symmetry mixing with topological symmetries and connecting 4D operator dimensions to 3D accidental symmetries.

Findings

Reproduction of S^3 partition functions from superconformal indices

Identification of imaginary mass deformations linked to topological symmetries

Connection between 4D operator dimensions and 3D accidental symmetries

Abstract

In a recent paper, we proposed closed-form expressions for the superconformal indices of the (A_1, A_{2n-3}) and (A_1, D_{2n}) Argyres-Douglas (AD) superconformal field theories (SCFTs) in the Schur limit. Following up on our results, we turn our attention to the small S^1 regime of these indices. As expected on general grounds, our study reproduces the S^3 partition functions of the resulting dimensionally reduced theories. However, we show that in all cases---with the exception of the reduction of the (A_1, D_4) SCFT---certain imaginary partners of real mass terms are turned on in the corresponding mirror theories. We interpret these deformations as R symmetry mixing with the topological symmetries of the direct S^1 reductions. Moreover, we argue that these shifts occur in any of our theories whose four-dimensional N=2 superconformal U(1)_R symmetry does not obey an SU(2) quantization condition. We then use our R symmetry map to find the four-dimensional ancestors of certain three-dimensional operators. Somewhat surprisingly, this picture turns out to imply that the scaling dimensions of many of the chiral operators of the four-dimensional theory are encoded in accidental symmetries of the three-dimensional theory. We also comment on the implications of our work on the space of general N=2 SCFTs.