Infinitely many N=1 dualities from $m+1-m=1$

TL;DR

<3-5 sentence high-level summary>This work constructs two infinite families of 4d ${\cal N}=1$ SCFTs, ${T}_N^{(m)}$ and ${\cal U}_N^{(m)}$, from the 6d ${\cal N}=(2,0)$ theory via class ${\cal S}$, allowing negative-degree line bundles on the UV curve. It shows that for all $m>0$, the RG flow of ${\cal U}_N^{(m)}$ lands at the same IR fixed point as ${SU}(N)$ SQCD with $N_f=2N$ and a quartic superpotential, so each ${\cal U}_N^{(m)}$ provides a distinct UV completion dual to SQCD. The paper exploits nilpotent Higgsing, a-maximization, and the superconformal index to establish operator maps, anomaly matching, and index equivalences across an array of dual frames, including quiver representations with up to $2m+1$ gauge nodes. It also generalizes the construction to ${SU}(N)$ theories, offering insights into a web of dualities and suggesting avenues for extensions to other gauge groups and puncture structures.

Abstract

We discuss two infinite classes of 4d supersymmetric theories, ${T}_N^{(m)}$ and ${\cal U}_N^{(m)}$, labelled by an arbitrary non-negative integer, $m$. The ${T}_N^{(m)}$ theory arises from the 6d, $A_{N-1}$ type ${\cal N}=(2,0)$ theory reduced on a 3-punctured sphere, with normal bundle given by line bundles of degree $(m+1, -m)$; the $m=0$ case is the ${\cal N}=2$ supersymmetric $T_N$ theory. The novelty is the negative-degree line bundle. The ${\cal U}_N^{(m)}$ theories likewise arise from the 6d ${\cal N}=(2,0)$ theory on a 4-punctured sphere, and can be regarded as gluing together two (partially Higgsed) ${T}_N^{(m)}$ theories. The ${T}_N^{(m)}$ and ${\cal U}_N^{(m)}$ theories can be represented, in various duality frames, as quiver gauge theories, built from $T_N$ components via gauging and nilpotent Higgsing. We analyze the RG flow of the ${\cal U}_N^{(m)}$ theories, and find that, for all integer $m>0$, they end up at the same IR SCFT as $SU(N)$ SQCD with $2N$ flavors and quartic superpotential. The ${\cal U}_N^{(m)}$ theories can thus be regarded as an infinite set of UV completions, dual to SQCD with $N_f=2N_c$. The ${\cal U}_N^{(m)}$ duals have different duality frame quiver representations, with $2m+1$ gauge nodes.

Figures (30)

• Figure 1: Dual descriptions ${\cal U}_N^{(m)}$ of $SU(N)$ SQCD with $2N$ flavors. Here $m=2$, where $m$ refers to the number of white nodes on both sides of the black node in the middle. Black circular nodes denote ${\cal N}=1$ vector multiplets, and white circular nodes denote ${\cal N}=2$ vector multiplets. As usual, square nodes denote global symmetries.
• Figure 2: Some examples of the quiver diagram describing the $T_N^{(m)}$ theories. In general, there is a number of dual descriptions for the $T_N^{(m)}$ theory itself.
• Figure 3: An example of colored pair-of-pants decomposition. Here red/blue means $\sigma=\pm$ respectively. Three red punctures and two blue punctures with $p=2, q=1$. Grey tube denotes ${\cal N}=1$ vector, white tube denotes ${\cal N}=2$ vector multiplet. There are 3 punctures of opposite color. There is an adjoint chiral multiplet attached to each of them.
• Figure 4: The UV description corresponding to the colored pair-of-pants description of figure \ref{['fig:pDecompEx']}. Here we assumed all punctures to be maximal.
• Figure 5: Higgsing the punctures to get the UV curve with lower degrees.