Abstract
Argyres-Douglas theories constitute an important class of superconformal field theories in 4d. The main focus of this paper is on two infinite families of such theories, known as {D}_p^b (SO(2N)) and (Am, Dn). We analyze in depth their conformal manifolds. In doing so we encounter several theories of class \U0001d4ae of twisted Aodd, twisted Aeven and twisted D types associated with a sphere with one twisted irregular puncture and one twisted regular puncture. These models include Dp(G) theories, with G non-simply-laced algebras. A number of new properties of such theories are discussed in detail, along with new SCFTs that arise from partially closing the twisted regular puncture. Moreover, we systematically present the 3d mirror theories, also known as the magnetic quivers, for the {D}_p^b (SO(2N)) theories, with p ≥ b, and the (Am, Dn) theories, with arbitrary m and n. We also discuss the 3d reduction and mirror theories of certain {D}_p^b (SO(2N)) theories, with p < b, where the former arises from gauging topological symmetries of some {T}_p^{sigma } [SO(2M)] theories that are not manifest in the Lagrangian description of the latter.
Highlights
Superconformal field theories (SCFTs) in four spacetime dimensions and with eight supercharges attracted much interest over the past decades, as the conformal symmetry and the large amount of supersymmetry often make it possible to achieve exact results even in the strongly coupled regime.One interesting class of such SCFTs are those of Argyres-Douglas (AD) type
5 Dp2N−2(SO(2N )) with p ≥ 2N − 2 and GCD(2N − 2, p) odd. All theories in this class do not have any mass parameters in addition to those associated with the SO(2N ) flavor symmetry
We provide some explicit examples of non-Higgsable SCFTs, together with their values of 24(c − a) and their ranks in appendix C
Summary
Superconformal field theories (SCFTs) in four spacetime dimensions and with eight supercharges attracted much interest over the past decades, as the conformal symmetry and the large amount of supersymmetry often make it possible to achieve exact results even in the strongly coupled regime. Despite being interacting and non-Lagrangian, many AD theories are not isolated They can admit exactly marginal operators in the spectrum, and possess a conformal manifold. Our focus is double: we systematically study the structure of the conformal manifold of this class of models, as well as derive their 3d mirror theories [14] upon reduction on a circle. As a consequence of the analysis of the 3d mirrors, we find that the dimensional reduction of E6 Minahan-Nemeschansky (MN) theory [29] admits a UV completion as USp(4) with 5 flavors plus a gauging of the U(1) topological symmetry We argue that such topological symmetry is present from the existence of monopole operators of conformal dimension 1. For the sake of the readers, we summarize the 4d theories studied in this paper together with their definitions in table 1
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