Comments on the symmetry of AdS${}_6$ solutions in String/M-theory and Killing spinor equations

Abstract

It was recently pointed out in \cite{Kim:2015hya} that AdS${}_6$ solutions in IIB theory enjoy an extended symmetry structure and the consistent truncation to $D=4$ internal space leads to a nonlinear sigma model with target $SL(3,\mathbb{R})/SO(2,1)$. We continue to study the purely bosonic $D=4$ effective action, and elucidate how the addition of scalar potential term still allows Killing spinor equations in the absence of gauge fields. In particular, the potential turns out to be a single diagonal component of the coset representative. Furthermore, we perform a general analysis of the integrability conditions of Killing spinor equations and establish that the effective action can be in fact generalized to arbitrary sizes and signatures, e.g. with target $SL(n,\mathbb{R})/SO(p,n-p)$ and the scalar potential expressible by a single diagonal component of the coset representative. We also comment on a similar construction and its generalizations of effective $D=5$ purely bosonic non-linear sigma model action related to AdS${}_6$ in M-theory.

v2: 17 pages, version published in PLB

References in corpus (2)

• AdS_6 solutions of type II supergravity
• Supersymmetric AdS_6 Solutions of Type IIB Supergravity

Cited by in corpus (21)

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• Exact results for 5d SCFTs of long quiver type
• Entanglement entropy vs. free energy in IIB supergravity duals for 5d SCFTs
• Testing $Ad{S}_6/CF{T}_5$ in Type IIB with stringy operators
• Janus solutions in six-dimensional gauged supergravity
• $Ad{S}_6$ T-duals and Type IIB $Ad{S}_6\times S^2$ Geometries with 7-Branes
• Massive spin 2 excitations in $Ad{S}_6\times S^2$ warped spacetimes
• Type IIB 7-branes in warped $Ad{S}_6$: partition functions, brane webs and probe limit
• Black hole microstate counting in Type IIB from 5d SCFTs
• Mass deformations of 5d SCFTs via holography
• $Ad{S}_2\times S^6$ versus $Ad{S}_6\times S^2$ in Type IIB supergravity
• AdS${}_6$/CFT${}_5$ with O7-planes
• Wrapped Brane Solutions in Romans $F(4)$ Gauged Supergravity
• M-theory curves from warped AdS${}_6$ in Type IIB
• On minimal Type IIB $Ad{S}_6$ solutions with commuting 7-branes
• Relating AdS${}_6$ solutions in type IIB supergravity
• Uplifting supersymmetric $Ad{S}_6$ black holes to type II supergravity
• AdS${}_6$ T-duals and AdS${}_6\times S^2$ geometries in Type IIB
• Non-Integrability of Strings in $Ad{S}_6\times S^2\times \Sigma$ Background and its 5D Holographic Duals