Higgsing and Twisting of 6d $D_N$ gauge theories

TL;DR

The article develops Type IIB 5-brane web constructions that realize 6d $\mathcal{N}=(1,0)$ SCFTs with $SO(N)$ gauge symmetry on a circle, derived from RG flows on Higgs branches of $D$-type conformal matter and cross-checked against Calabi–Yau threefold geometries. It advances non-toric brane web techniques involving O5-planes and KK-momentum–driven Higgs flows to produce twisted compactifications, including $Z_2$ twists, and explicitly matches monopole-string tensions to CY$_3$ prepotentials across a wide set of examples on $-3$, $-2$, and $-4$ curves. The paper provides a comprehensive catalog of untwisted and twisted brane webs for $SO(N)$ and related algebras ($G_2$, $SU(3)$) on these curves, establishing a robust bridge between brane constructions and CY geometries for 6d circle-compactified theories. It also introduces novel RG flows triggered by KK modes that yield consistent twisted theories, offering new avenues for exploring twisted 6d compactifications and potential extensions to exceptional gauge sectors.

Abstract

We propose Type IIB 5-brane configurations that engineer the 6d $\mathcal{N}=(1,0)$ SCFTs with $SO(N)$ gauge symmetry coupled to a single tensor multiplet on a circle, by considering RG flows on Higgs branches of $D$-type conformal matter theories. We test the brane systems against known Calabi-Yau threefolds for the 6d SCFTs on a circle. In addition we study a new RG flow involving Higgs vevs of scalar operators with Kaluza-Klein momentum along the circle. The new RG flow results in the 5-brane webs for the 6d SCFTs of $D_N$ gauge symmetry compactified on a circle with $Z_2$ outer-automorphism twist.

Figures (35)

• Figure 1: Two surfaces (or 4-cycles) $S_1=\mathbb{F}_{n_1,g_1}^{p_1}$ and $S_2=\mathbb{F}_{n_2,g_2}^{p_2}$ glued along a curve $C$ whose projection to the surface $S_i$ is denoted by $C_i$. The subscript of $|_i$ denotes $i$-th surface.
• Figure 2: (a) 5-brane web for a local $\mathbb{P}^2$. (b) A 5-brane web for $\mathbb{F}^1_1=\mathbb{F}_0^1$. (c) A 5-brane web for two surfaces $S_1=\mathbb{F}_1$ and $S_2 = \mathbb{F}_3$.
• Figure 3: (a) A local 5-brane web for an $\mathbb{F}_n$. (b) A 5-brane web for $\mathbb{F}^1_3$. (c) A 5-brane web for $\mathbb{F}_3^2$.
• Figure 4: (a) The 5-brane web for a non-toric threefold of two intersecting surfaces $S_1=\mathbb{F}_3$ and $S_2=\mathbb{F}_5$. (b) The 5-brane web for a non-toric threefold of $S_1=\mathbb{F}_1$ and $S_2=\mathbb{F}_5$ which is the resulting 5-brane web after the Hanany-Witten transition is implemented on the 5-brane web (a) with $(-1,1)$ 7-brane.
• Figure 5: (a) A non-toric threefold of four surfaces $\mathbb{F}_2\cup \mathbb{F}_0 \cup \mathbb{F}_2 \cup \mathbb{F}_2$. (b) The brane web for the threefold (a). This is also a brane web for the 5d $SU(8)$ gauge theory at low energy.