Compactifications of 5d SCFTs with a twist

TL;DR

<3-5 sentence high-level summary>The paper investigates how 5d SCFTs compactified on a circle with twists by discrete global symmetries yield 4d N=2 isolated SCFTs, including known theories such as the rank-1 SU(4)SCFT and new ones with symmetries like F4, G2, and E7. The authors develop a framework based on brane-web constructions and Hall-Littlewood indices to identify the 4d theories, study their Higgs branches, mass deformations, and dualities, and to validate proposals through explicit index computations. They uncover a rich web of dualities linking twisted reductions to known Lagrangian and non-Lagrangian frames, and they propose HL-index formulas for twisted theories that align with the Hilbert spaces of the corresponding Higgs branches. The results suggest deep connections to class-S constructions and S-folds, and point to many potential new 4d SCFTs awaiting further exploration and geometric realization.

Abstract

We study the compactification of 5d SCFTs to 4d on a circle with a twist in a discrete global symmetry element of these SCFTs. We present evidence that this leads to various 4d N=2 isolated SCFTs. These include many known theories as well as seemingly new ones. The known theories include the recently discovered rank 1 SU(4) SCFT and its mass deformations. One application of the new SCFTs is in the dual descriptions of the 4d gauge theory SU(N)+1S+(N-2)F. Also interesting is the appearance of a theory with rank 1 and $F_4$ global symmetry.

Figures (47)

• Figure 1: (a) The brane web for an $SU_0(2)$ gauge theory. The arrow shows the distance corresponding in the gauge theory to the inverse gauge coupling squared. (b) Taking the $\frac{1}{g^2}\rightarrow 0$ limit leads to the web describing the $5d$ SCFT. (c) The web for $\frac{1}{g^2}< 0$. Note that performing S-duality leads us back to the original theory so this limit also has a low-energy description as an $SU_0(2)$ gauge theory.
• Figure 2: A $5d$ SCFT with an $SU(N)^2\times SU(k)^2\times U(1)$ global symmetry.
• Figure 3: The brane web representation of a $5d$ SCFT, described by the collapsed web. (a) A deformation of the SCFT illustrating the $2F+SU(2)\times SU(2)+2F$ gauge theory description. (b) The S-dual web now illustrating the $SU_0(3)+6F$ gauge theory description.
• Figure 4: (a) The brane web representation of a $5d$ SCFT, generated from the one in figure \ref{['Ils1']} by gauging both $SU(2)$ global symmetries. (b) A mass deformation of the SCFT corresponding to the limit $g^{-2}_{SU(2)}\rightarrow \infty$ where $g_{SU(2)}$ is the coupling constant of both edge $SU(2)$ gauge groups. (c) The mass deformation corresponding to the limit $g^{-2}_{SU(2)}\rightarrow -\infty$ where we have also performed S-duality on the web. That this deformation is a continuation of the previous one is apparent as it preserves the $U(6)$ global symmetry. In this limit the $SU(2)$ quiver description is inadequate, but there is a different description as an $SU_0(5)+6F$ gauge theory where this limit corresponds to $g^{-2}_{SU(5)}\rightarrow \infty$ for $g_{SU(5)}$ being the coupling constant of $SU(5)$.
• Figure 5: (a) The brane web representation of a $5d$ SCFT, generated from the one in figure \ref{['Ils1']} by double gauging an $SU(3)+1F$ into the $SU(6)$ global symmetry. (b) A mass deformation of the SCFT corresponding to the limit $g^{-2}_{SU(3)}\rightarrow \infty$ where $g_{SU(3)}$ is the coupling constant of both edge $SU(3)$ gauge groups. (b) The mass deformation corresponding to the limit $g^{-2}_{SU(3)}\rightarrow -\infty$ where we have also performed S-duality on the web. That this deformation is a continuation of the previous one is apparent as it preserves the $U(2)^2\times U(1)^2$ global symmetries associated with the semi-infinite $5$-branes. In this limit the $SU(3)$ quiver description is inadequate, but there is a different description as an $2F+SU_0(4)\times SU_0(4)+2F$ gauge theory where this limit corresponds to $g^{-2}_{SU(4)}\rightarrow \infty$ for $g_{SU(4)}$ the coupling constant of both $SU(4)$ gauge groups.