Abstract
We extend the investigation of the recently introduced class ${\cal S}_k$ of 4d $\mathcal{N}=1$ SCFTs, by considering a large family of quiver gauge theories within it, which we denote $\mathcal{S}^1_k$. These theories admit a realization in terms of $\mathbb{Z}_k$ orbifolds of Type IIA configurations of D4-branes stretched among relatively rotated sets of NS-branes. This fact permits a systematic investigation of the full family, which exhibits new features such as non-trivial anomalous dimensions differing from free field values and novel ways of gluing theories. We relate these ingredients to properties of compactification of the 6d (1,0) superconformal ${\cal T}_N^k$ theories on spheres with different kinds of punctures. We describe the structure of dualities in this class of theories upon exchange of punctures, including transformations that correspond to Seiberg dualities, and exploit the computation of the superconformal index to check the invariance of the theories under them.
Highlights
In recent years, a successful incarnation of this general program has been to consider compactifications of 6d SCFTs to engineer SCFTs in various dimensions and with different amounts of SUSY
An even broader N = 1 generalization, denoted class Sk, was recently proposed in [26]. It is defined as the compactification of the 6d (1,0) SCFTs TkN 1, which arise from N M5-branes at an Ak−1 orbifold singularity in M-theory, over punctured Riemann surfaces
In this paper we introduce a new class of 4d N = 1 SCFTs, which we call class Sk1, and which fall in the class of Sk described by compactifications of 6d (1,0) SCFTs TkN on punctured Riemann surfaces Σ
Summary
We will construct class Sk1 quiver theories, which are defined in terms of Type IIA brane configurations of D4-branes stretched among mutually rotated NS5-branes [25] (building on [4]). A Type I node corresponds to N D4-branes stretched between an NS-NS’ pair, and contains an SU (N ) gauge factor, bifundamental chiral multiplets Xi,i±1, Xi±1,i, and a quartic superpotential interaction among them, given (modulo sign) by 4. A Type II node corresponds to N D4-branes stretched between an NS-NS or an NS’-NS’ pair, and contains an SU (N ) gauge factor, bifundamental chiral multiplets Xi,i±1, Xi±1,i, one adjoint chiral multiplet Φi, and a cubic superpotential (modulo sign). In these quivers, every oriented plaquette corresponds to a term in the superpotential. The non-dynamical adjoint Φ0 gives rise to k non-dynamical bifundamental fields φ((00,,aa−) 1) between pairs of global nodes They are coupled to chiral bifundamental fields connected to the first column of gauge nodes through cubic superpotential terms of the form. We will combine the basic building blocks we have discussed above into full theories
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