6d SCFTs, 5d Dualities and Tao Web Diagrams

TL;DR

This work develops a cohesive framework linking 6d ${\cal N}=(1,0)$ SCFTs realized in Type IIA string theory (with an $O8^-$ plane) to a rich landscape of 5d ${\cal N}=1$ gauge theories obtained via circle compactification and T-duality, expressed as Tao 5-brane webs with two $O7^-$ planes. It identifies three distinct sources of 5d dualities—SU-$Sp$ duality from $O7^-$-plane resolution, distribution duality from brane placement, and $SL(2,\mathbb{Z})$-duality from web rotations—demonstrating that many different 5d descriptions share the same 6d UV fixed point, including flavor-decoupled variations. The paper extends these dualities to broad classes of 6d sp–su and SU quivers, analyzes Higgsing patterns, and provides a 6d description for generalized 5d Tao theories (T_N Tao) that in some cases lie outside standard Type IIA realizations. It also exploits 7-brane monodromies to extract global symmetries and shows how S-duality and higher SL(2,\mathbb{Z}) transformations generate a web of equivalent 5d frames with identical UV completions, offering new routes to compute indices and BPS spectra across dual frames. Overall, the results illuminate a rich, interconnected map between 6d SCFTs and a family of 5d dual gauge theories, with potential applications to novel dual pairs, flavor decouplings, and higher-dimensional generalizations.

Abstract

We propose 5d descriptions of 6d ${\cal N}=(1,0)$ superconformal field theories arising from Type IIA brane configurations with an $O8^-$-plane. We T-dualize the brane diagram along a compactification circle and obtain a 5-brane web diagram with two $O7^-$-planes. The gauge theory description of the resulting 5d theory for a given 6d superconformal field theory is not unique, and we argue that the non-uniqueness leads to various dual 5d gauge theories. There are three sources which lead to the 5d dualities. One type comes from either resolving both or one of the two $O7^-$-planes. The two situations give us two different ways to read off a 5d gauge theory from essentially the same web diagram. The second type originates from different distributions of D5 or D7-branes, shifting the gauge group ranks of the 5d quiver theory. The last one comes from the 90 or 45 degree rotations of the 5-brane web diagram, which is a part of the $SL(2,\mathbb{Z})$ duality of Type IIB string theory, leading to completely different group structure. These lead to a very rich class of dualities between 5d gauge theories whose UV completion is the same 6d superconformal field theory. We also explore Higgsing of the 6d theories and their 5d counterparts. Decoupling the same flavors from the dual 5d theories gives rise to another dual 5d theories whose UV completion is the same 5d superconformal field theory. Finally we propose the 6d description of 5d theories which is obtained by a generalization of 5d $T_N$ theories with additional flavors, which turns out not to be in the class of Type IIA brane construction generically.

Figures (53)

• Figure 1: Left: Type IIA brane realization of the $(D_{N+4}, D_{N+4})$ minimal conformal matter in the tensor branch. Right: The quiver diagram of the 6d theory.
• Figure 2: Type IIB brane descriptions for 6d ${\mathcal{N}}=(1,0)$$Sp(N)$ gauge theory with one tensor multiplet and $2N+8$ flavors in the fundamental representation, which yields ${\mathcal{N}}=1$$SU(N+2)$ gauge theory with the number of flavors. The horizontal direction is $x^6$ and the vertical direction is the T-dualized direction. For simplicity, $N=1$. Left: The brane configuration with two $O7^-$ planes. A dashed line denotes the branch cut of 7-brane, while a dash-dot line denotes the mirror reflection cut of an $O7^-$ plane. Middle: The brane configuration with two $O7^-$ planes which are non-perturbatively resolved. Here we denote $\mathbf{A}$ for a D7 brane, $\mathbf{B}$ for a $[1,-1]$ 7-brane, and $\mathbf{C}$ for a $[1,1]$ 7-brane. Right: Pulling out 7-branes gives rise to a web configuration for $SU(3)$ gauge theory with $N_f=10$ flavors and zero CS level.
• Figure 3: Tao diagram for 5d $\mathcal{N}=1$$SU(3)$ gauge theory with $N_f=10$ flavors which is a circle compactification of 6d $\mathcal{N}=(1,0)$$Sp(1)$ gauge theory with one tensor multiplet and $10$ flavors. The rightmost brane configuration on Figure \ref{['Fig:IIB']} can be reorganized to be the leftmost web configuration given here, using 7-brane monodromies. Pulling out 7-branes passing through the branch cut of other 7-branes gives a Tao wed diagram on the rightmost.
• Figure 4: Type IIB brane descriptions for 6d ${\mathcal{N}}=(1,0)$$Sp(N)$ gauge theory with one tensor multiplet and $2N+8$ flavors in the fundamental representation, which yields ${\mathcal{N}}=1$$Sp(N+1)$ gauge theory with the number of flavors. For simplicity, $N=1$. Left: The brane configuration with two $O7^-$ planes. Middle: The brane configuration with only one of two $O7^-$ planes is resolved. Right: The resulting $Sp(2)$ gauge theory with $N_f=10$ flavors.
• Figure 5: The S-dual of $SU(3)$ theory with $N_f=10$ flavor is $SU(2)\times SU(2)$ quiver theory with $N_f=4$ flavors to each $SU(2)$ theory of the quiver.