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Register a new user3d mirrors of the circle reduction of twisted $A_{2N}$ theories of class $mathsf{S}$
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Mirror symmetry has proven to be a powerful tool to study several properties of higher dimensional superconformal field theories upon compactification to three dimensions. We propose a quiver description for the mirror theories of the circle reduction of twisted $A_{2N}$ theories of class $mathsf{S}$ in four dimensions. Although these quivers bear a resemblance to the star-shaped quivers previously studied in the literature, they contain unitary, symplectic and special orthogonal gauge groups, along with hypermultiplets in the fundamental representation. The vacuum moduli spaces of these quiver theories are studied in detail. The Coulomb branch Hilbert series of the mirror theory can be matched with that of the Higgs branch of the corresponding four dimensional theory, providing a non-trivial check of our proposal. Moreover various deformations by mass and Fayet-Iliopoulos terms of such quiver theories are investigated. The fact that several of them flow to expected theories also gives another strong support for the proposal. Utilising the mirror quiver description, we discover a new supersymmetry enhancement renormalisation group flow.
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In the reduction of 4d dualities to 3d there are non-perturbative effects arising from monopoles acting as instantons. This mechanism has been reproduced in string theory by engineering the theories in a IIA brane setup. Nevertheless there are limiting cases of the 4d dualities where the dual theories are actually confined phases of the UV gauge theories. In these cases the monopoles are absent and the mechanism of reduction of the 4d duality has to be modified. In this paper we investigate such modification in the brane setup. The main observation behind our analysis is that in the 4d case the superpotential of the confined theories can been obtained also as the exotic contribution of a D0 brane, a stringy instanton. When considering these configurations we reproduce the field theory results in the brane setup. We study both the unitary and the symplectic case. As a further check we study the reduction of the 4d superconformal index to the 3d partition function for these theories.
Argyres-Douglas theories constitute an important class of superconformal field theories in $4$d. The main focus of this paper is on two infinite families of such theories, known as $D^b_p(mathrm{SO}(2N))$ and $(A_m, D_n)$. We analyze in depth their conformal manifolds. In doing so we encounter several theories of class $mathcal{S}$ of twisted $A_{text{odd}}$, twisted $A_{text{even}}$ and twisted $D$ types associated with a sphere with one twisted irregular puncture and one twisted regular puncture. These models include $D_p(G)$ 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 $3$d mirror theories, also known as the magnetic quivers, for the $D^b_p(mathrm{SO}(2N))$ theories, with $p geq b$, and the $(A_m, D_n)$ theories, with arbitrary $m$ and $n$. We also discuss the $3$d reduction and mirror theories of certain $D^b_p(mathrm{SO}(2N))$ theories, with $p < b$, where the former arises from gauging topological symmetries of some $T^sigma_rho[mathrm{SO}(2M)]$ theories that are not manifest in the Lagrangian description of the latter.
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We study the Coulomb branch of class $mathcal{S}_k$ $mathcal{N} = 1$ SCFTs by constructing and analyzing their spectral curves.
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