More on 5d descriptions of 6d SCFTs

TL;DR

This work presents a systematic construction of five-dimensional ${\cal N}=1$ gauge theories that UV-complete six-dimensional ${\cal N}=(1,0)$ SCFTs realized in type IIA string theory with an ${ON^0}$-plane. By deploying T-duality, S-duality, and novel resolutions of ${O7^-}$-planes, the authors generate a rich set of 5d quiver theories with $SO$, $Sp$, and $SU$ gauge groups, including a new duality between a D-type $SU$ quiver and an $SO$-$Sp$ linear quiver. The paper also analyzes twisted circle compactifications, yielding 5d theories distinct from ordinary circle reductions and revealing twisted affine flavor symmetries such as $A_{2N-1}^{(2)}$. Across multiple orientifold configurations involving ${ON^0}$, ${O6}$, and ${O8}$ planes, the authors demonstrate consistent matching of Coulomb-branch dimensions and flavor/mass parameters between the 5d descriptions and their 6d UV completions, supported by instanton analyses and brane-web techniques. Overall, the results expand the landscape of UV-complete 5d theories and provide new dualities and construction methods for 6d/5d correspondences in string theory.

Abstract

We propose new five-dimensional gauge theory descriptions of six-dimensional $\mathcal{N}=(1,0)$ superconformal field theories arising from type IIA brane configurations including an $ON^0$-plane. The new five-dimensional gauge theories may have $SO$, $Sp$, and $SU$ gauge groups and further broaden the landscape of ultraviolet complete five-dimensional $\mathcal{N}=1$ supersymmetric gauge theories. When we include an $O8^-$-plane in addition to an $ON^0$-plane, T-duality yields two $O7^-$-planes at the intersections of an $ON^0$-plane and two $O5^0$-planes. We propose a novel resolution of the $O7^-$-plane with four D7-branes in such a configuration, which enables us to obtain three different types of five-dimensional gauge theories, depending on whether we resolve either none or one or two $O7^-$-planes. Such different possibilities yield a new five-dimensional duality between a D-type $SU$ quiver and an $SO-Sp$ quiver theories. We also claim that a twisted circle compactification of a six-dimensional superconformal field theory may lead to a five-dimensional gauge theory different from those obtained by a simple circle compactification.

Figures (39)

• Figure 1: (a): The brane configuration of two D5-branes and an $O5^-$-plane on a Coulomb branch of the $SO(4)$ gauge theory. The red lines denote the fundamental strings which yield gauge fields in the $SO(4)$ gauge theory. (b): The S-dual diagram to the figure (a). The orange lines denote NS5-branes. The D1-branes between the $ON^-$-plane and the NS5$_2$ looks separated pictorially but they are coincident.
• Figure 2: (a): The proposal of the microscopic description of an $ON^0$-plane. (b): A shorthand picture of the figure (a). We often make use of this picture in the later sections for simplicity but it always means figure (a).
• Figure 3: A microscopic description of an $ON^0$-plane with multiple NS5-branes. We also add two semi-infinite D5-branes at the right end for later use. We will call this configuration split D5-branes on an $ON^0$-plane.
• Figure 4: (a): The S-dual to the Figure \ref{['fig:ONmNS5']}. (b): Another alternative brane configuration including an $O5^+$-plane.
• Figure 5: (a): The brane configuration with an unsplit NS5-brane attached to the $O5^-$-plane. This configuration is obtained by moving $N$ D5-branes to the place of $O5^-$ plane from Figure \ref{['fig:5ddualbase']} (a). (b): An NS5-brane split on $O5^-$ plane into two fractional ones. An $O5^+$ plane are created between the two fractional NS5-branes. This configuration is obtained analogously from Figure \ref{['fig:5ddualbase']} (b).