Perturbative Hairy Black Branes in the G2-Invariant Sector of Dyonic ISO(7) Gauged Supergravity
Abstract
We construct perturbative black-brane solutions carrying neutral scalar hair in the G2-invariant truncation of four-dimensional dyonic 𝒩=8 ISO(7) gauged supergravity, an exact consistent truncation of massive type~IIA supergravity on S6. Expanding around the G2-symmetric AdS4-Schwarzschild black brane in powers of a dimensionless scalar-charge parameter eps, we show that the perturbation hierarchy reduces, order by order, to a nested sequence of inhomogeneous Legendre equations (demonstrated through second order). The first-order scalar satisfies a Pöschl--Teller equation with exact parameter ν(ν+1)=2/3, giving ν=−1/2+√(33)/6, and the first-order metric is fixed algebraically by the same function, A(1)=−√7/2ϕ(1), so the entire 𝒪(eps) sector is one Legendre function. An identity ν+1=Δ+/3, with Δ+=(3+√(33))/2≈ 4.372 the conformal dimension of the dual scalar operator, relates the Pöschl-Teller parameter to the AdS/CFT dictionary via the nonlinear Fefferman-Graham map z ∝ zFG3. The 𝒪(eps2) back-reaction yields explicit corrections to the renormalized free energy and Bekenstein-Hawking entropy density at fixed temperature, consistent with the first law; equivalently, at fixed entropy or energy density it \emph{lowers} the Hawking temperature by δT/T=𝒪(eps2). For the leading transport coefficients the shear viscosity saturates η/s=1/(4π), while the Eling-Oz horizon formula gives a nonzero bulk viscosity ζ/η=((Δ+−3)/2)2eps2=(3(7−√(33)))/8eps2≈0.471 eps2. With cs2=1/2−𝒪(eps2)<1/2, this indicates a softening of the equation of state.
Related
- Maximal D=5 trombone supergravity from M5-branes and SU(2)-flavoured 𝒩=1 class 𝒮 operator spectra
- D4-branes wrapped on topological disks from matter-coupled F(4) gauged supergravity
- Perturbative dynamics and relativistic effects of a dyonic Kalb-Ramond black hole
- Perturbative Nicolai-Map Diagrammatics: Application to Poincaré Supergravity
- Gauge-invariant thermodynamic description of rotating black strings in 5D minimal supergravity via Kaluza-Klein reduction
BibTeX
@misc{yun2026perturbative,
title = {{Perturbative Hairy Black Branes in the $G_2$-Invariant Sector of Dyonic ISO(7) Gauged Supergravity}},
author = {Sangheon Yun},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.18959},
eprint = {2608.18959},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.18959},
}
RIS
TY - UNPB
TI - Perturbative Hairy Black Branes in the G_2-Invariant Sector of Dyonic ISO(7) Gauged Supergravity
AU - Sangheon Yun
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2608.18959
UR - https://arxiv.org/abs/2608.18959
AB - We construct perturbative black-brane solutions carrying neutral scalar hair in the G_2-invariant truncation of four-dimensional dyonic 𝒩=8 ISO(7) gauged supergravity, an exact consistent truncation of massive type~IIA supergravity on S^6. Expanding around the G_2-symmetric AdS_4-Schwarzschild black brane in powers of a dimensionless scalar-charge parameter eps, we show that the perturbation hierarchy reduces, order by order, to a nested sequence of inhomogeneous Legendre equations (demonstrated through second order). The first-order scalar satisfies a Pöschl--Teller equation with exact parameter ν(ν+1)=2/3, giving ν=−1/2+√(33)/6, and the first-order metric is fixed algebraically by the same function, A^(1)=−√7/2ϕ^(1), so the entire 𝒪(eps) sector is one Legendre function. An identity ν+1=Δ_+/3, with Δ_+=(3+√(33))/2≈ 4.372 the conformal dimension of the dual scalar operator, relates the Pöschl-Teller parameter to the AdS/CFT dictionary via the nonlinear Fefferman-Graham map z ∝ z_FG^3. The 𝒪(eps^2) back-reaction yields explicit corrections to the renormalized free energy and Bekenstein-Hawking entropy density at fixed temperature, consistent with the first law; equivalently, at fixed entropy or energy density it \emph{lowers} the Hawking temperature by δT/T=𝒪(eps^2). For the leading transport coefficients the shear viscosity saturates η/s=1/(4π), while the Eling-Oz horizon formula gives a nonzero bulk viscosity ζ/η=((Δ_+−3)/2)^2eps^2=(3(7−√(33)))/8eps^2≈0.471 eps^2. With c_s^2=1/2−𝒪(eps^2)<1/2, this indicates a softening of the equation of state.
ER -