More on the N=2 superconformal systems of type $D_p(G)$

TL;DR

This paper provides a detailed analysis of a large family of 4d N=2 superconformal field theories labeled as Dp(G), computing their key physical quantities, identifying known subclasses, and exploring their BPS chambers and dualities.

Contribution

It introduces a functorial approach using META-quivers, computes central charges and flavor groups for all Dp(G) models, and identifies their relation to known SCFTs and fixed points.

Findings

Computed central charges a, c, k, and flavor group F for all Dp(G) models.

Identified subclasses corresponding to known SCFTs and fixed points.

Proved three conjectures by Xie and Zhao, and checked Argyres-Seiberg duality.

Abstract

A large family of 4d N=2 SCFT's was introduced in arXiv:1210.2886. Its elements $D_p(G)$ are labelled by a positive integer p\in N and a simply-laced Lie group G; their flavor symmetry is at least G. In the present paper we study their physics in detail. We also analyze the properties of the theories obtained by gauging the diagonal symmetry of a collection of $D_{p_i}(G)$ models. In all cases the computation of the physical quantities reduces to simple Lie-theoretical questions. To make the analysis more functorial, we replace the notion of the BPS-quiver of the N=2 QFT by the more intrinsic concept of its META-quiver. In particular: 1) We compute the SCFT central charges a, c, k, and flavor group F for all $D_p(G)$ models. 2) We identify the subclass of $D_p(G)$ theories which correspond to previously known SCFT's (linear SU and SO-USp quiver theories, Argyres-Douglas models, superconformal gaugings of Minahan-Nemeshanski E_r models, etc.), as well as to non-trivial IR fixed points of known theories. The $D_p(E_r)$ SCFT's with $p\geq 3$ cannot be constructed by any traditional method. 3) We investigate the finite BPS chambers of some of the models. 4) As a by product, we prove three conjectures by Xie and Zhao, and provide new checks of the Argyres-Seiberg duality.