Lifting 4d dualities to 5d

TL;DR

The paper develops a bridge between 4d isolated ${\cal N}=2$ SCFTs and 5d ${\cal N}=1$ gauge theories by constructing 5d Lagrangian descriptions via 5-brane webs for families such as ${T_N}$, ${R_{0,N}}$, and ${\chi_N^k}$, among others. It shows that many 5d gauge dualities correspond to 4d ${\cal N}=2$ S-dualities, enabling explicit checks of dualities and enhanced global symmetries through the 5d superconformal index, including instanton-generated currents that realize symmetry enhancements like ${SU(N)^3}$, ${SU(8)}$, and ${SO(14)}$. The work provides detailed mappings of global charges and BPS spectra across the 5d/4d reductions in several landmark cases (e.g., ${SU(3)+6}$, ${SU(N)+2N}$, and higher quivers), and discusses the conditions under which 5d dualities yield 4d dualities. It also outlines a broad program for extending these techniques to additional families and for deriving precise coupling maps. Overall, the results offer a practical framework for translating between 4d dualities and 5d gauge dynamics via brane webs and indices, with clear implications for understanding UV fixed points of higher-rank theories.

Abstract

In this paper we set out to further explore the connection between isolated N=2 SCFT's in four dimensions and N=1 SCFT's in five dimensions. Using 5-brane webs we are able to provide IR Lagrangian descriptions in terms of 5d gauge theories for several classes of theories including the so-called TN theories. In many of these we find multiple dual gauge theory descriptions. The connection to 4d theories is then used to lift 4d N=2 S-dualities that involve weakly-gauging isolated theories to 5d gauge theory dualities. The 5d description allows one to study the spectrum of BPS operators directly, using for example the superconformal index. This provides additional non-trivial checks of enhanced global symmetries and 4d dualities.

Figures (42)

• Figure 1: The 5-brane web of the $T_N$ theory (shown for $N=5$): (a) Fixed point theory (b) on the Coulomb branch.
• Figure 2: Another web for $T_N$ ($N=5$): (a) After an HW transition (b) Mass deforming to reveal the gauge theory (the shaded regions correspond to the gauge groups) (c) The S-dual web.
• Figure 3: Quiver diagram for the IR gauge theory of $T_N$.
• Figure 4: Deforming the $SU(n)+2n$ ($n=3$ in this case) sub-web to compute the CS level.
• Figure 5: Higgs branch: When the positions of two 7-branes transverse to the 5-branes that end on them coincide, one of the 5-branes can break.