Quiver Tails and N=1 SCFTs from M5-branes

TL;DR

This work studies four-dimensional ${\cal N}=1$ SCFTs arising from M5-branes on punctured Riemann surfaces (class ${\cal S}$) and introduces a new building block, the Fan, which emerges from nilpotent Higgsing of ${\cal N}=1$ quivers. The Fan enables the construction of ${\cal N}=1$ quiver tails and facilitates dual descriptions, including an ${\cal N}=1$ Argyres-Seiberg-type dual for SU($N$) SQCD with $2N$ flavors via a pair-of-pants exchange involving a $T_N$ sector. The authors compute 't Hooft anomalies and the superconformal index for theories with Fans and demonstrate exact matches across dual frames, providing strong checks of the duality web. Overall, the Fan offers a geometric UV description of ${\cal N}=1$ class ${\cal S}$ theories and expands the landscape of calculable invariants, with future directions toward more general punctures and gravity duals.

Abstract

We study a class of four-dimensional N=1 superconformal field theories obtained by wrapping M5-branes on a Riemann surface with punctures. We identify UV descriptions of four-dimensional SCFTs corresponding to curves with a class of punctures. The quiver tails appearing in these UV descriptions differ significantly from their N=2 counterpart. We find a new type of object that we call the `Fan'. We show how to construct new N=1 superconformal theories using the Fan. Various dual descriptions for these SCFTs can be identified with different colored pair-of-pants decompositions. For example, we find an N=1 analog of Argyres-Seiberg duality for the SU(N) SQCD with 2N flavors. We also compute anomaly coefficients and superconformal indices for these theories and show that they are invariant under dualities.

Figures (22)

• Figure 1: An example of a generic $SU(N)$ quiver theory corresponding to the UV curve given by a sphere with two maximal and a number of minimal punctures. Note that the colored pair-of-pants mapped to the bifundamentals, and the tubes mapped to the gauge nodes.
• Figure 2: The Seiberg dual of the quiver given by figure \ref{['fig:GenLinearQuiver']} and its colored pair-of-pants decomposition. Here we dualized the right-most gauge group $SU(N)_1$. Note that the second gauge group $SU(N)_2$ became ${\cal N}=1$ because of the meson dual to $Q_1 \widetilde{Q}_1$ behaves as an extra adjoint chiral, which generates a mass term for the adjoint chiral. From the UV curve viewpoint, this is represented by that the colors of the second and third pairs-of-pants are different.
• Figure 3: An ${\cal N}=2$ linear quiver theory.
• Figure 4: An ${\cal N}=2$ quiver theory obtained after Higgsing specified by the partition $N = \sum_{k=1}^5 n_k k$. The ranks of the gauge groups are fixed by conformality condition $2N_i = N_{i-1} + N_{i+1} + n_i$.
• Figure 5: A generic form of the Fan given by $(N, N')$ and the partition $N-N' = \sum_{k=1}^5 k n_k$.