Wrapping M5-branes on a non-spin manifold: Spinh structures and AdS7 black holes
Abstract
We construct a solution of seven-dimensional maximal gauged supergravity of the form AdS2× M5, where M5 is the five-dimensional Wu manifold $SU(3)/SO(3)$. The solution is supersymmetric, despite the fact that the Wu manifold admits neither a spin structure nor a spinc structure. Rather, it admits a spinh structure, wherein the ill-definedness of ordinary spinors due to a minus sign in their holonomy is compensated by a further minus sign arising through the spinors carrying SO(3) Yang-Mills charge, in a half-integer isospin representation of the SU(2) double cover of the SO(3). We show how the configuration can be lifted to a solution of D=11 supergravity of the form AdS2× M9, where M9 is the unit tangent bundle of the Wu manifold. We discuss the geometry and topology of M9, and study the supersymmetry from the eleven-dimensional standpoint. We extend the seven-dimensional solution to a black hole, and discuss some aspects of its holographic interpretation and the UV to IR flow. We revisit a previously-known AdS2× H3× H2 solution, and its UV to IR flow, showing that the flow equations in fact admit of an exact solution. Additionally, we give a detailed discussion of the lift of the AdS2× S5 solution to D=11, exhibiting similarities and differences between the properties of its internal space M9 (the unit tangent bundle of S5) and the Wu manifold example of our main discussion. We also construct the non-compact dual of the Wu manifold solution, where M5 is taken to be SL(3,ℝ)/SO(3).
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BibTeX
@misc{gibson2026wrapping,
title = {{Wrapping M5-branes on a non-spin manifold: Spin$^h$ structures and AdS$_7$ black holes}},
author = {Cameron Gibson and Okan Günel and C. N. Pope},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24084},
eprint = {2610.24084},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24084},
}
RIS
TY - UNPB
TI - Wrapping M5-branes on a non-spin manifold: Spin^h structures and AdS_7 black holes
AU - Cameron Gibson
AU - Okan Günel
AU - C. N. Pope
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.24084
UR - https://arxiv.org/abs/2610.24084
AB - We construct a solution of seven-dimensional maximal gauged supergravity of the form AdS_2× M_5, where M_5 is the five-dimensional Wu manifold $SU(3)/SO(3)$. The solution is supersymmetric, despite the fact that the Wu manifold admits neither a spin structure nor a spin^c structure. Rather, it admits a spin^h structure, wherein the ill-definedness of ordinary spinors due to a minus sign in their holonomy is compensated by a further minus sign arising through the spinors carrying SO(3) Yang-Mills charge, in a half-integer isospin representation of the SU(2) double cover of the SO(3). We show how the configuration can be lifted to a solution of D=11 supergravity of the form AdS_2× M_9, where M_9 is the unit tangent bundle of the Wu manifold. We discuss the geometry and topology of M_9, and study the supersymmetry from the eleven-dimensional standpoint. We extend the seven-dimensional solution to a black hole, and discuss some aspects of its holographic interpretation and the UV to IR flow. We revisit a previously-known AdS_2× H^3× H^2 solution, and its UV to IR flow, showing that the flow equations in fact admit of an exact solution. Additionally, we give a detailed discussion of the lift of the AdS_2× S^5 solution to D=11, exhibiting similarities and differences between the properties of its internal space M_9 (the unit tangent bundle of S^5) and the Wu manifold example of our main discussion. We also construct the non-compact dual of the Wu manifold solution, where M_5 is taken to be SL(3,ℝ)/SO(3).
ER -