More on the $ \mathcal{N}=2 $ superconformal systems of type D p (G)

Abstract

A large family of 4d N = 2 SCFT's was introduced in 1210.2886. Its elements D p (G) are labelled by a positive integer p ∈ 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-U Sp 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 ≥ 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.

Geometric engineering, mirror symmetry and 6 d 1 0 → 4 d N = 2 $$ 6{\mathrm{d}}_{\left(1,0\right)}\to 4{\mathrm{d}}_{\left(\mathcal{N}=2\right)} $$

“…JHEP11 (2015)123 which is exactly the SW geometry for D p (SU(n)) [13][14][15]. Proceeding analogously, replacing Z n with Γ a DE subgroup of SU (2), one obtains…”

“…SCFTs which are A, D and E gauge theories where the matter involves gauging three or four copies of D p (G = ADE) [13][14][15] (which are generalizations of D-type Argyres-Douglas theories, which have SU(2) global symmetry, to theories with arbitrary A, D and E global symmetries). Also the N = 2 vacuum geometry for some theories we study is captured by an LG period geometry rather than a curve or a local Calabi-Yau 3-fold.…”

“…The resulting SCFTs were introduced in [15] as generalization of the findings of [60] in the G = SU(2) case. We denote them by (E (1,1) n , G), n = 4, 6, 7, 8.…”

“…These models are examples of the E (1,1) n G systems constructed in [15] where this other notation was used to emphasize that the product is not a standard product in between quivers, because the elliptic quivers have non-trivial potential.…”

“…Coulomb mass marginal Relevant BPS quiver parameter Since these theories all have exactly marginal deformations, we would like to find a weakly coupled gauge theory description: this is precisely how these models have been introduced in [15]. In such S-duality frame these systems have the following form:…”