Linear Quivers and N=1 SCFTs from M5-branes

TL;DR

The paper studies linear quivers built from {N=1}/{N=2} vector multiplets and hypermultiplets, arguing they flow to interacting IR SCFTs whose central charges are computable via a-maximization. It provides a detailed dual description in Type IIA brane setups and their M-theory uplift as M5-branes on a punctured sphere, with IR theories labeled by {κ,z,ℓ,N}. The central charges depend only on these discrete parameters, and the work uncovers dualities, a conformal manifold of marginal couplings, and hints at holographic regimes in the large-ℓ limit. The geometric M5-brane picture offers a pathway to generalize to new N=1 building blocks akin to T_N and to explore broader classes of quivers beyond the linear case.

Abstract

We study a class of N=1 quiver gauge theories build out of vector multiplets and matter multiplets in the fundamental and bifundamental representations. We argue that these theories flow to interacting SCFTs in the IR and calculate their central charges. We exhibit a type IIA brane construction which at low energies is described by these SCFTs. This also leads to a natural description of the theories in terms of M5-branes on a punctured sphere.

Figures (5)

• Figure 1: A general linear quiver. The shaded and unshaded circles denote $\mathcal{N}=1$ and $\mathcal{N}=2$ vector multiplets respectively. The lines connecting them are hypermultiplets in the bifundamental of the $SU(N)$ gauge groups at the two ends of the line. The boxes at both ends of the quiver represent two sets of $N$ hypermultiplets in the fundamental of the $SU(N)$ gauge group.
• Figure 2: A simple linear quiver with $\ell=3$ (a) and its Seiberg dual when there is no superpotential turned on (b). After Seiberg duality the mesons charged under the $\mathcal{N}=2$ vector multiplet are represented as a fundamental hypermultiplet and a chiral adjoint.
• Figure 3: A configuration of intersecting D4- and NS5-branes which corresponds to a linear quiver. The horizontal black lines represent a stack of $N$ D4-branes extended along the $x_6$ direction. The vertical black lines are the $v$ NS5-branes extended along $x_{4,5}$. The blue lines represent the $w$ NS5-branes extended along $x_{7,8}$. All branes extend along the 4D space-time directions $x_{0,1,2,3}$ and are localized at $x_9=0$.
• Figure 4: The sphere with seven minimal and two maximal punctures which corresponds to $\ell=7$. We have taken four minimal punctures of type $v$ or $\sigma=+1$ (in black) and three minimal punctures of type $w$ or $\sigma=-1$ (in blue). We have $\kappa=1$ (two black maximal punctures) on the left, $\kappa=-1$ (two blue maximal punctures) in the middle and $\kappa=0$ (one black and one blue maximal puncture) on the right.
• Figure 5: The sphere with two maximal and one minimal puncture. The picture on the left corresponds to a hypermultiplet in the bifundamental of $SU(N)\times SU(N)$. The other two pictures do not have a simple interpretation in field theory but should correspond to isolated $\mathcal{N}=1$ SCFTs.