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} 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.
Highlights
Superconformal theories with eight supercharges in four dimension represent an interesting laboratory for the exploration of strongly-coupled dynamics in field theory
We study several new aspects of AD theories engineered in A-type class S with one irregular puncture of Type I or Type II and 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
The main goal is to show that, at a generic point of the Higgs branch, the theory can be reduced to a set of hypermultiplets plus a collection of superconformal theories (SCFTs) with empty Higgs branch
Summary
Superconformal theories with eight supercharges in four dimension represent an interesting laboratory for the exploration of strongly-coupled dynamics in field theory. The most commonly used ones are the class S construction [12] and the geometric engineering in Type IIB via compactification on singular Calabi-Yau threefolds [7, 8] Both methods play a key role in the present paper and provide a detailed description of the Coulomb branch of these theories. The new ingredient at the heart of our analysis is the recent observation of [34] that the above-mentioned class of AD theories becomes lagrangian upon dimensional reduction, being equivalent to a linear quiver with unitary and special unitary gauge groups. Their number is related to the dimension of the Higgs branch, as will be derived in section 2 from the Type IIB geometric engineering of AD theories These non higgsable theories without a Higgs branch become twisted hypermultiplets upon dimensional reduction and via mirror symmetry become a collection of free hypermultiplets.
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