Wrapped D4-branes from maximal 6D gauged supergravity

TL;DR

This work constructs and analyzes a broad class of holographic domain-wall solutions in six-dimensional maximal gauged supergravity with CSO gaugings, focusing on twisted compactifications on Riemann surfaces and three-manifolds that yield Mkw_3×Σ^2 and Mkw_2×Σ^3 slices. By employing topological twists and embedding-tensor techniques, the authors derive BPS equations for wrapped D4-brane configurations, explore various gauge groups (including CSO(p,q,5-p-q) and CSO(p,q,4-p-q)⋉ℝ^4), and classify IR geometries via physically acceptable singularities using Gubser and Maldacena–Nunez criteria. The solutions interpolate between locally flat UV domain walls and curved IR walls, and, upon uplift to type IIA, are interpreted as D4-branes wrapped on Σ^2 and Σ^3, describing holographic RG flows across dimensions from five-dimensional to three-/two-dimensional non-conformal field theories. The results map a rich landscape of dual QFTs, provide analytic and numerical examples, and point to future work on complete type IIA truncations and broader spindle/spindle-like compactifications within EFT frameworks.

Abstract

We study a large class of domain wall solutions with $Mkw_3\times Σ^2$ and $Mkw_2\times Σ^3$ slices from maximal gauged supergravity in six dimensions. $Σ^2$ and $Σ^3$ are given by a Riemann surface and a $3$-manifold with constant curvature while $Mkw_{3,2}$ denotes three/two-dimensional Minkowski space. We consider the maximal gauged supergravity with $CSO(p,q,5-p-q)$ and $CSO(p,q,4-p-q)\ltimes \mathbb{R}^4$ gauge groups arising from an $S^1$ reduction of seven-dimensional maximal gauged supergravity with $CSO(p,q,5-p-q)$ and $CSO(p,q,4-p-q)$ gauge groups. The two types of gauge group can be embedded in type IIA theory via consistent truncations on $H^{p,q}\times \mathbb{R}^{5-p-q}$ and $H^{p,q}\times\mathbb{R}^{4-p-q}\times S^1$, respectively. By performing topological twists on $Σ^2$ and $Σ^3$, we find a number of solutions interpolating between locally flat domain walls in the UV and curved domain walls with $Mkw_3\times Σ^2$ and $Mkw_2\times Σ^3$ slices in the IR. Many solutions admit physical IR singularities and can be interpreted as holographic RG flows across dimensions from five-dimensional field theories to three- and two-dimensional non-conformal field theories in the IR. Upon uplifted to type IIA theory, we expect the solutions to describe brane configurations involving D4-branes wrapped on $Σ^2$ and $Σ^3$.

Figures (53)

• Figure 1: Interpolating solutions between the locally $SO(5)$ flat domain wall as $\rho\rightarrow+\infty$ and $Mkw_3\times S^2$-sliced curved domain walls for $SO(2)\times SO(2)$ twist in $SO(5)$ gauge group. The blue, orange, green, red, and purple curves refer to $p_1=-2, 0, 0.1, 0.5, 1.3$, respectively.
• Figure 2: Interpolating solutions between the locally $SO(5)$ flat domain wall as $\rho\rightarrow+\infty$ and $Mkw_3\times H^2$-sliced curved domain walls for $SO(2)\times SO(2)$ twist in $SO(5)$ gauge group. The blue, orange, green, red, and purple curves refer to $p_1=-8, -2.4, -0.5, 0, 2.6$, respectively.
• Figure 3: Interpolating solutions between the locally $SO(5)$ flat domain wall as $\rho\rightarrow+\infty$ and $Mkw_3\times \mathbb{R}^2$-sliced curved domain walls for $SO(2)\times SO(2)$ twist in $SO(5)$ gauge group. The blue, orange, green, red, and purple curves refer to $p_1=-2, -2\times10^{-5}, -2\times10^{-9}, 10^{-7}, 0.1$, respectively. The dashed curve is the $SO(2)\times SO(2)$ flat domain wall obtained from setting $p_1=0$ which also implies $p_2=k=0$.
• Figure 4: The behavior of $\hat{g}_{00}$ along the RG flows given in figures \ref{['15_S2_special_SO(2)xSO(2)_SO(5)gg_flows']}, \ref{['15_H2_special_SO(2)xSO(2)_SO(5)gg_flows']}, and \ref{['15_R2_special_SO(2)xSO(2)_SO(5)gg_flows']}, respectively for $\Sigma^2=S^2, H^2, \mathbb{R}^2$ in $SO(5)$ gauge group.
• Figure 5: Interpolating solutions between the locally $SO(2)\times SO(2)$ flat domain wall as $\rho\rightarrow+\infty$ and $Mkw_3\times S^2$-sliced curved domain walls for $SO(2)\times SO(2)$ twist in $SO(5)$ gauge group. The blue, orange, green, red, and purple curves refer to $p_1=-5, -2.94, -0.90, 1.90, 1.91$, respectively.