Holography, Brane Intersections and Six-dimensional SCFTs

TL;DR

This work analyzes supersymmetric intersections of NS5-, D6-, and D8-branes in massive IIA, showing that a near-horizon limit reproduces the supersymmetric AdS$_7$ vacua classified in prior work. It leverages a consistent 7D minimal gauged supergravity truncation to construct a universal tensor-branch RG flow, interpreted as a vev for a dimension-4 operator in the 6d $N=(1,0)$ SCFT energy-momentum multiplet. The authors also obtain explicit upliftings: to eleven dimensions as M5-brane distributions and to massive IIA as intersecting brane solutions, including a massless NS5-D6 configuration whose near-horizon geometry matches AdS$_7$. The results highlight a universal structure of tensor-branch deformations in 6d SCFTs and raise questions about D8 effects, singularity resolution, and connections to lower-dimensional compactifications.

Abstract

We study supersymmetric intersections of NS5-, D6- and D8-branes in type IIA string theory. We focus on the supergravity description of this system and identify a "near horizon" limit in which we recover the recently classified supersymmetric seven-dimensional AdS solutions of massive type IIA supergravity. Using a consistent truncation to seven-dimensional gauged supergravity we construct a universal supersymmetric deformation of these AdS vacua. In the holographic dual six-dimensional (1,0) superconformal field theory this deformation describes a universal RG flow on the tensor branch of the vacuum moduli space triggered by a vacuum expectation value for a protected scalar operator of dimension four.

Figures (6)

• Figure 1: An illustrative example of the system of intersecting branes discussed in the main text and in Table \ref{['table:intersection']}.
• Figure 2: A brane configuration that should be described by the conformal limit of a linear quiver gauge theory.
• Figure 3: The solution (\ref{['massivey']}-\ref{['cubic']}) with $M g_s=-3$, $c_1=7/3$ and $c_2 = -6$. The coordinate range for $\alpha$ is $[-5/9,4/9]$. Notice that $y^2$ is a decreasing function of $\alpha$ because of the negative mass and that it takes non-zero values at both poles indicating the presence of D6-branes at both poles.
• Figure 4: An example of the solution of (\ref{['massivey']}-\ref{['cubic']}) with $M g_s=2$, $c_1=3$ and $c_2 = 0$. The geometry has a stack of D6 branes at one pole, $\alpha=3$, but is regular at the other pole, $\alpha=-3/2$. The function $y(\alpha)$ has a non-zero value at $\alpha=3$ but vanishes at $\alpha=-3/2$ indicating that only one of the poles has D6 branes.
• Figure 5: A solution of \ref{['AdsODE']} with two D8 brane singularities. The mass parameters are $M^{(1)}g_s=3$, $M^{(2)}g_s=1$ and $M^{(3)}g_s=0$ and determine the slope of the linear function $y^2$. The other integration constants are $c_1^{(1)}=c_1^{(2)}=c_1^{(3)}-1=5$, $c_2^{(1)}=-10$ and $\alpha_+^{(1)}=\alpha_+^{(2)}-1=0$. The remaining constants can be obtained by the continuity of $\alpha$, $\beta$ and $y$. The coordinate $\alpha$ ranges from $\alpha_-^{(1)}\approx -1.51$ to $\alpha^{(3)}_+ \approx 2.11$. The reason, only approximate values are given is that these are obtained by setting $\beta(\alpha)=0$ and are therefore solutions to cubic and quadratic equations respectively.