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AdS$_7$/CFT$_6$ with orientifolds

Fabio Apruzzi, Marco Fazzi

TL;DR

The paper advances AdS$_7$/CFT$_6$ holography by incorporating orientifolds (O6 and O8) into massive IIA brane constructions, enabling SO/USp quivers alongside SU quivers. It provides a unified holographic framework where the AdS$_7$ vacua are encoded by a single cubic polynomial α$(z)$, and demonstrates that the leading $a$ anomaly from supergravity precisely matches the holographic limit of the six-dimensional anomaly polynomial for a broad class of tensor-branch theories. Several new gravity duals are constructed, including vacua dual to F-theory quivers and to formal (non-perturbative) IIA configurations, with explicit $a$-anomaly calculations. Finally, a holographic $a$-theorem for Higgs-branch RG flows is proposed, supported by monotonic behavior of a simple gravity-side quantity, reinforcing the consistency of AdS$_7$/CFT$_6$ in the presence of orientifolds and non-trivial quiver data.

Abstract

AdS$_7$ solutions of massive type IIA have been classified, and are dual to a large class of six-dimensional $(1,0)$ SCFT's whose tensor branch deformations are described by linear quivers of SU groups. Quivers and AdS vacua depend solely on the group theory data of the NS5-D6-D8 brane configurations engineering the field theories. This has allowed for a direct holographic match of their $a$ conformal anomaly. In this paper we extend the match to cases where O6 and O8-planes are present, thereby introducing SO and USp groups in the quivers. In all of them we show that the $a$ anomaly computed in supergravity agrees with the holographic limit of the exact field theory result, which we extract from the anomaly polynomial. As a byproduct we construct special AdS$_7$ vacua dual to nonperturbative F-theory configurations. Finally, we propose a holographic $a$-theorem for six-dimensional Higgs branch RG flows.

AdS$_7$/CFT$_6$ with orientifolds

TL;DR

The paper advances AdS/CFT holography by incorporating orientifolds (O6 and O8) into massive IIA brane constructions, enabling SO/USp quivers alongside SU quivers. It provides a unified holographic framework where the AdS vacua are encoded by a single cubic polynomial α, and demonstrates that the leading anomaly from supergravity precisely matches the holographic limit of the six-dimensional anomaly polynomial for a broad class of tensor-branch theories. Several new gravity duals are constructed, including vacua dual to F-theory quivers and to formal (non-perturbative) IIA configurations, with explicit -anomaly calculations. Finally, a holographic -theorem for Higgs-branch RG flows is proposed, supported by monotonic behavior of a simple gravity-side quantity, reinforcing the consistency of AdS/CFT in the presence of orientifolds and non-trivial quiver data.

Abstract

AdS solutions of massive type IIA have been classified, and are dual to a large class of six-dimensional SCFT's whose tensor branch deformations are described by linear quivers of SU groups. Quivers and AdS vacua depend solely on the group theory data of the NS5-D6-D8 brane configurations engineering the field theories. This has allowed for a direct holographic match of their conformal anomaly. In this paper we extend the match to cases where O6 and O8-planes are present, thereby introducing SO and USp groups in the quivers. In all of them we show that the anomaly computed in supergravity agrees with the holographic limit of the exact field theory result, which we extract from the anomaly polynomial. As a byproduct we construct special AdS vacua dual to nonperturbative F-theory configurations. Finally, we propose a holographic -theorem for six-dimensional Higgs branch RG flows.

Paper Structure

This paper contains 54 sections, 187 equations, 6 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Brane configurations in massive IIA and supergravity solutions
  3. The dictionary between branes, quivers, and vacua
  4. Only SU(k) groups: M5's on C2/Zk
  5. Alternating SO-USp groups: M5's in C2/Dk
  6. SO or USp flavor, USp, SO, SU gauge groups: O8+- onto D8's
  7. The holographic limit
  8. Constructing generic solutions with $z$
  9. Boundary conditions
  10. Computation of $a$ in field theory
  11. SU quivers on the tensor branch
  12. Alternating SO-USp quivers on the tensor branch
  13. Quivers from brane configurations with an O8-plane
  14. Computation of a in O8+ and D8-O8- theories
  15. Quivers from brane configurations with O6-planes and an O8-plane
  16. ...and 39 more sections

Figures (6)

  • Figure 1: Brane configurations and quivers for $\mathop{\mathrm{SU}}\nolimits$ gauge and flavor groups.
  • Figure 2: Brane configurations and quivers for alternating $\mathop{\mathrm{SO}}\nolimits$-$\mathop{\mathrm{USp}}\nolimits$ gauge and flavor groups.
  • Figure 3: Possible NS5-D6-D8-O8 brane configurations without O6-planes or extra D8-branes.
  • Figure 4: Quivers engineered by NS5-D6-D8-O8$^\pm$ brane configurations. Notice that we have added possible flavors for each gauge node for $i=1,\ldots,N-1$. ($f_0=g_0=2n_0$ is the rank of the leftmost flavor $\mathop{\mathrm{USp}}\nolimits / \mathop{\mathrm{SO}}\nolimits$ group respectively.) This can be done as long as condition \ref{['eq:ti-gaugeanom']} is satisfied at each node. We use same colors and names as those in figures \ref{['fig:quiverNS5D6D8']} and \ref{['fig:quiverNS5D6O6D8']}. In figures \ref{['fig:massiveE']} and \ref{['fig:quiver-massiveE']} we see the brane engineering and the quiver describing the rank-$N$ massive E-string theory.
  • Figure 5: Possible NS5-D6-O6-D8-O8 brane configurations and the linear quivers they engineer.
  • ...and 1 more figures