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Brane webs and $O5$-planes

Gabi Zafrir

TL;DR

This work demonstrates that brane webs in orientifold $O5$ backgrounds robustly realize 5d fixed-point theories, including alternating $SO$ and $USp$ quivers and $D$-shaped $SU$ quivers, and enables engineering of $SO(N)$ theories with spinor matter through a nonperturbative mechanism. By analyzing Higgs branches, S-duality, and dualities, the authors uncover symmetry enhancements and map between different low-energy gauge descriptions, with explicit checks using the 5d superconformal index. The results provide a concrete framework for studying fixed points, dualities, and instanton-driven phenomena in these theories, and hint at possible six-dimensional uplifts. Overall, the paper extends the toolkit for constructing and validating 5d SCFTs via brane webs in orientifold backgrounds and highlights nonperturbative spinor matter as a key ingredient.

Abstract

We explore the properties of five-dimensional supersymmetric gauge theories living on $5$-brane webs in orientifold $5$-plane backgrounds. This allows constructing quiver gauge theories with alternating $USp(2N)$ and $SO(N)$ gauge groups with fundamental matter, and thus leads to the existence of new $5d$ fixed point theories. The web description can be further used to study non-perturbative phenomena such as enhancement of symmetry and duality. We further suggest that one can use these systems to engineer $5d$ $SO$ group with spinor matter. We present evidence for this claim.

Brane webs and $O5$-planes

TL;DR

This work demonstrates that brane webs in orientifold backgrounds robustly realize 5d fixed-point theories, including alternating and quivers and -shaped quivers, and enables engineering of theories with spinor matter through a nonperturbative mechanism. By analyzing Higgs branches, S-duality, and dualities, the authors uncover symmetry enhancements and map between different low-energy gauge descriptions, with explicit checks using the 5d superconformal index. The results provide a concrete framework for studying fixed points, dualities, and instanton-driven phenomena in these theories, and hint at possible six-dimensional uplifts. Overall, the paper extends the toolkit for constructing and validating 5d SCFTs via brane webs in orientifold backgrounds and highlights nonperturbative spinor matter as a key ingredient.

Abstract

We explore the properties of five-dimensional supersymmetric gauge theories living on -brane webs in orientifold -plane backgrounds. This allows constructing quiver gauge theories with alternating and gauge groups with fundamental matter, and thus leads to the existence of new fixed point theories. The web description can be further used to study non-perturbative phenomena such as enhancement of symmetry and duality. We further suggest that one can use these systems to engineer group with spinor matter. We present evidence for this claim.

Paper Structure

This paper contains 15 sections, 20 equations, 34 figures.

Table of Contents

  1. Introduction
  2. The general construction
  3. $O5^+$ and USp groups
  4. $O5^-$ and SO groups
  5. $\tilde{O5}$
  6. $SO \times USp$ quivers
  7. S-duality and $O5^0$-plane
  8. Spinor matter
  9. Dualities
  10. Example $1$
  11. Example $2$
  12. Example $3$
  13. Conclusions
  14. Index computation
  15. $SO \times USp$

Figures (34)

  • Figure 1: (a) The classical picture of a half NS5-brane crossing an $O5$-plane, represented as a black dashed line. (b) The quantum picture, where bending occurs so that the D5-brane charge is conserved.
  • Figure 2: Brane webs for pure $USp(2N)$ gauge theory using an $O5^+$-plane. (a) Shows the $N=1$ case while (b) shows the general case.
  • Figure 3: Examples of webs for a $USp$ gauge theory with fundamental flavor. (a) Shows the case of $USp(4)+4F$ while (b) shows the general case of $USp(2N)+(N_{F_L} + N_{F_R})F$.
  • Figure 4: (a) The brane web for $SU_0(2)$, also known as the $E_1$ theory, at a generic coupling and at a generic point on the Coulomb branch (on the left), and at the origin of the Coulomb branch and taking the bare coupling to infinity (on the right), describing the fixed point. We have also explicitly drawn the $7$-branes, shown as black circles. These span the $8$ directions coming out of the picture. (b) The brane web for $SU_{\pi}(2)$, also known as the $\tilde{E}_1$ theory. The web on the left is for a generic coupling and at a generic point on the Coulomb branch, and the the web on the right is at the origin of the Coulomb branch and taking the bare coupling to infinity. One note that there is no Higgs branch in this case. (c) The web of figure \ref{['fgr3']} (a) at the origin of the Coulomb branch and infinite coupling constant.
  • Figure 5: (a) The web for $USp(2)+2F$. (b) The web at the origin of the Coulomb branch and for massless flavor, after the D7-branes were separated along the $O5$-plane. (c) The web at a generic point on the Higgs branch. For ease of presentation we have used a different view of the web where the vertical straight lines are the D5-branes, the horizontal wide lines are the D7-branes, and the black dot is the (1,-1) 5-brane.
  • ...and 29 more figures