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Dualities and 5-brane webs for 5d rank 2 SCFTs

Hirotaka Hayashi, Sung-Soo Kim, Kimyeong Lee, Futoshi Yagi

TL;DR

The work constructs comprehensive 5-brane web realizations for the rank-2 5d SCFTs classified by geometry, enabling explicit duality maps between $G_2$, $SU(3)$, and $Sp(2)$ theories across various flavor contents. By exploiting S-duality and Hanany–Witten transitions with 7-branes and orientifold planes, the authors derive parameter mappings for masses and Coulomb moduli, and they confirm these via matching monopole tensions to prepotentials. The analysis uncovers a rich network of marginal theories, including $G_2+6\mathbf{F}$, $SU(3)_{3/2}+9\mathbf{F}$, and $Sp(2)+1\mathbf{AS}+8\mathbf{F}$, with periodic Tao-like webs signaling 6d UV completions. The results provide a concrete brane-based framework to study dualities, mass deformations, and 6d uplifts of 5d SCFTs, and suggest avenues for BPS counting, indices, and higher-rank generalizations.

Abstract

We consider Type IIB 5-brane configurations for 5d rank 2 superconformal theories which are classified recently by geometry in arXiv:1801.04036. We propose all the 5-brane web diagrams for these rank 2 theories and show dualities between some of different gauge theories with explicit duality map of mass parameters and Coulomb branch moduli. In particular, we explicitly construct 5-brane configurations for $G_2$ gauge theory with six flavors and its dual $Sp(2)$ and $SU(3)$ gauge theories. We also present 5-brane webs for $SU(3)$ theories of Chern-Simons level greater than 5.

Dualities and 5-brane webs for 5d rank 2 SCFTs

TL;DR

The work constructs comprehensive 5-brane web realizations for the rank-2 5d SCFTs classified by geometry, enabling explicit duality maps between , , and theories across various flavor contents. By exploiting S-duality and Hanany–Witten transitions with 7-branes and orientifold planes, the authors derive parameter mappings for masses and Coulomb moduli, and they confirm these via matching monopole tensions to prepotentials. The analysis uncovers a rich network of marginal theories, including , , and , with periodic Tao-like webs signaling 6d UV completions. The results provide a concrete brane-based framework to study dualities, mass deformations, and 6d uplifts of 5d SCFTs, and suggest avenues for BPS counting, indices, and higher-rank generalizations.

Abstract

We consider Type IIB 5-brane configurations for 5d rank 2 superconformal theories which are classified recently by geometry in arXiv:1801.04036. We propose all the 5-brane web diagrams for these rank 2 theories and show dualities between some of different gauge theories with explicit duality map of mass parameters and Coulomb branch moduli. In particular, we explicitly construct 5-brane configurations for gauge theory with six flavors and its dual and gauge theories. We also present 5-brane webs for theories of Chern-Simons level greater than 5.

Paper Structure

This paper contains 30 sections, 94 equations, 137 figures.

Table of Contents

  1. Introduction
  2. $G_2$-$SU(3)$-$Sp(2)$ sequence
  3. Without matter
  4. With matter
  5. Duality to $SU(3)_6 + 2{\bf F}$
  6. Duality to $Sp(2)_{\pi} + 2{\bf AS}$
  7. Duality among marginal theories
  8. Duality to $SU(3)$.
  9. Duality to $Sp(2)$.
  10. Realization as $SO(5) + 2{\bf V} + 4{\bf S}$
  11. $SU(3)$-$Sp(2)$-$SU(2)\times SU(2)$ sequences
  12. Deformation to 5-brane web of $SU(3)_{\frac{3}{2}} + 9 {\bf F}$, $Sp(2) +1 {\bf AS} + 8{\bf F}$ and $[5\mathbf{F}+SU(2)]\times[SU(2)+2\mathbf{F}]$
  13. Duality between $Sp(2)+ 1\mathbf{AS}+8\mathbf{F}$ and $SU(3)_{\frac{3}{2}}+ 9\mathbf{F}$
  14. $SU(2)\times SU(2)$ quiver description.
  15. Duality map between $SU(3)_{\frac{3}{2}} + 9 {\bf F}$ and $Sp(2) +1 {\bf AS} + 8{\bf F}$
  16. ...and 15 more sections

Figures (137)

  • Figure 1: (a): A 5-brane web diagram for the pure $G_2$ gauge theory which is realized with an $\widetilde{\text{O5}}$-plane. The orange line represents the $\widetilde{\text{O5}}$-plane. The convention of the $\widetilde{\text{O5}}$-plane is different from the one used in Hayashi:2018bkd. Here, the monodomry branch cut from a fractional D7-brane is extends from left to right whereas it extends from right to left in Hayashi:2018bkd. (b): The gauge theory parameterization of the pure $G_2$ diagram.
  • Figure 2: A 5-brane web diagram for the pure $SU(3)$ gauge theory with the CS level $7$. The green line represents an $\widetilde{\text{ON}}$-plane.
  • Figure 3: (a): The gauge theory parameterization for the 5-brane web diagram of the pure $SU(3)$ gauge theory in Figure \ref{['fig:pureSU3CS7']}. $a_1, a_2, a_3$ are the Coulomb branch moduli of $SU(3)$. The dotted line in the center is the location of the origin in the vertical direction. $m_0$ is the inverse of the squared gauge coupling. (b): A labeling for the faces in the 5-brane web in Figure \ref{['fig:pureSU3CS7']}.
  • Figure 4: (a): A 5-brane web diagram for the $G_2$ gauge theory with two flavors plus two singlets. The matter is originated from two spinors of a $SO(7)$ gauge theory before the Higgsing. (b): Another 5-brane web diagram for the $G_2$ gauge theory with two flavors and two singlets, which is obtained by performing a flop transition to the diagram in Figure \ref{['fig:G2w2flvrsa']}.
  • Figure 5: (a): The parameterization for the inverse of the squared gauge coupling $m_0$ and the Coulomb branch moduli $a_1, a_2$. (b): Two parameters $n_1, n_2$ related to mass parameters for the two flavors.
  • ...and 132 more figures