New aspects of Argyres-Douglas theories and their dimensional reduction

Abstract

Argyres-Douglas (AD) theories constitute an infinite class of superconformal field theories in four dimensions with a number of interesting properties. We study several new aspects of AD theories engineered in A-type class $$ \mathcal{S} $$ S with one irregular puncture of Type I or Type II and also a regular puncture. These include conformal manifolds, structures of the Higgs branch, as well as the three dimensional gauge theories coming from the reduction on a circle. We find that the latter admits a description in terms of a linear quiver with unitary and special unitary gauge groups, along with a number of twisted hypermultiplets. The origin of these twisted hypermultiplets is explained from the four dimensional perspective. We also propose the three dimensional mirror theories for such linear quivers. These provide explicit descriptions of the magnetic quivers of all the AD theories in question in terms of quiver diagrams with unitary gauge groups, together with a collection of free hypermultiplets. A number of quiver gauge theories presented in this paper are new and have not been studied elsewhere in the literature.

Conformal manifolds and 3d mirrors of Argyres-Douglas theories

“…Contrary to D b p (SU(N )) theories, whose reduction to 3d always leads to a Lagrangian theory [22,23], we do not have such a description for the class of theories studied in the present paper. As a result, the quiver description of each mirror theory in this paper is obtained by guesswork, based on information about the CB dimension, the value of JHEP08(2021)015 24(c − a) and the number of mass parameters of the original 4d theory in question.…”

“…Such conjectural quivers are then subject to several stringent tests, including matching of the HB and CB Hilbert series with those of the known theories in various special cases, as well as the Maruyoshi-Song (MS) flow [25] of the D b p (SO(2N )) theory. The latter deserves a more detailed discussion here, since it puts highly non-trivial constraints on the theory, as demonstrated in [22] for the D b p (SU(N )) theory. Roughly speaking, this is a renormalization group (RG) flow from the D p (SO(2N )) theory to the (A p−1 , D N ) theory [26], triggered by vacuum expectation values (VEVs) of certain flipping fields.…”

“…The presence of the free sector is explained by the fact that, at a generic point of the HB of the original 4d theory, the low-energy effective theory involves a sector of strongly coupled AD theories each of which does not have a HB. 1 In the same way as in [22], we refer to such a sector as the non-Higgsable SCFTs. These theories dimensionally reduce to free twisted hypermultiplets [22][23][24], which then correspond to the free hypermultiplets sector under the mirror map.…”

“…1 In the same way as in [22], we refer to such a sector as the non-Higgsable SCFTs. These theories dimensionally reduce to free twisted hypermultiplets [22][23][24], which then correspond to the free hypermultiplets sector under the mirror map.…”

5d and 4d SCFTs: canonical singularities, trinions and S-dualities

“…In this sense, the 3d reduction of D b p (SU(N )) is a 'Lagrangian theory'. 5 These 3d theories are also studied in [78].…”