New N=1 Dualities from M5-branes and Outer-automorphism Twists

TL;DR

The paper generalizes the GMTY construction by incorporating ${D_N}$-type outer-automorphism twists to produce ${ m N}=1$ SCFTs from M5-branes, yielding a rich web of dual frames for ${ m SO(2N)}/{ m USp(2N-2)}/{ m G_2}$ quivers. It introduces twisted building blocks ${T_{SO(2N)}}$ and ${ ilde{T}}_{SO(2N)}$, derives multiple Lagrangian and non-Lagrangian dual frames via colored pair-of-pants, and verifies dualities through 't Hooft anomaly matching and superconformal indices. Dual frames include electric, crossing, swapped, and Argyres-Seiberg-type descriptions, and their consistency is checked across ${ m SO}$, ${ m USp}$, and ${ m G}_2$ theories, with a notable symmetry enhancement to ${ m E}_7$ in the ${D_4}$ twisted setup. The work also demonstrates index computations, including ${ m N}=1$ indices derived from ${ m N}=2$ building blocks, to corroborate dualities and reveal enhanced flavor structures. Collectively, these results deepen the understanding of ${ m N}=1$ class ${ m S}$ theories and their duality networks, expanding the landscape of non-Lagrangian magnetic descriptions in four dimensions.

Abstract

We generalize recent construction of four-dimensional $\mathcal{N}=1$ SCFT from wrapping six-dimensional $\mathcal{N}=(2,0)$ theory on a Riemann surface to the case of $D$-type with outer-automorphism twists. This construction allows us to build various dual theories for a class of $\mathcal{N}=1$ quiver theories of $SO-USp$ type. In particular, we find there are five dual frames to $SO(2N)/USp(2N-2)/G_2$ gauge theories with $(4N-4)/4N/8$ fundamental flavors, where three of them are non-Lagrangian. We check the dualities by computing the anomaly coefficients and the superconformal indices. In the process we verify that the index of $D_4$ theory on a certain three punctured sphere with $Z_2$ and $Z_3$ twist lines exhibits the expected symmetry enhancement from $G_2 \times USp(6)$ to $E_7$.

Figures (29)

• Figure 1: The UV curves realizing SQCDs in this paper. The symbol ✘ denotes twisted null puncture, $\varocircle$ the full puncture having $SO(2N)$ flavor symmetry, the twisted full puncture having $USp(2N-2)$ flavor symmetry and $\heartsuit$ denotes $USp(4)$ puncture. The dashed line and the green solid line denote $\mathbb{Z}_2$ and $\mathbb{Z}_3$ twist line respectively.
• Figure 2: A choice of UV curve with colored punctures. Here we suppressed the labeling $\rho$ for each punctures.
• Figure 3: By twisting the punctures of $D_N$ theory, we get twisted punctures having the $C_{N-1}$ flavor symmetry.
• Figure 4: An example of colored pair-of-pants decomposition. Here red/blue means $\sigma=\pm$ respectively. Three red punctures and two blue punctures with $p=1, q=2$. Grey tube denotes ${\cal N}=1$ vector, white tube denotes ${\cal N}=2$ vector multiplet. We have 3 mesons associated to the blue puncture on the right and two red punctures on the left.
• Figure 5: Colored pair-of-pants decompositions for a 4-punctured sphere with two twisted full punctures and two twisted null punctures of each color. The degrees of normal bundles are $(p, q)=(1, 1)$. Each subscript stands for: crossing-type 1, swap, Argyres-Seiberg type, crossing-type 2. The first two dual frames have Lagrangian descriptions. The theory ${\cal U}^{SO}_{c1}$ turns out to be identical to the dual theory of Intriligator:1995id. The latter three theories are all non-Lagrangian theories. The theory ${\cal U}^{SO}_{s}$ is an $SO$ version of Gadde:2013fma.