# Warm Dark Matter from Higher-Dimensional Gauge Theories

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. keV WDM from Higher-Dimensional Gauge Theories

#### WDM Degrees of Freedom

## 3. Algebras with Higher-Dimensional Spinors

#### 3.1. Superalgebra in 17 + 1 and 9-Brane WV Reduction

#### 3.2. Superalgebra in 20 + 4 and 12-Brane WV Reduction

#### 3.2.1. Further Reduction in Inner/Fiber Symmetry

#### 3.2.2. Magic Star Reduction in D = 20 + 4

## 4. Symmetry Reduction to the Standard Model and Warm Dark Matter Disentanglement

#### 4.1. Braneworld Spinors

#### 4.2. Braneworld Intersections for Warm Dark Matter beyond the Standard Model

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MDPI | Multidisciplinary Digital Publishing Institute |

DOAJ | directory of open access journals |

WDM | warm dark matter |

CDM | cold dark matter |

SM | standard model |

EP | exceptional periodicity |

ESYM | exceptional super Yang–Mills |

WV | worldvolume |

## References

- Tikhonov, A.V.; Gottlöber, S.; Yepes, G.; Hoffman, Y. The sizes of minivoids in the local Universe: An argument in favour of a warm dark matter model? Mon. Not. RAS
**2009**, 399, 1611. [Google Scholar] [CrossRef] - Zavala, J.; Jing, Y.P.; Faltenbacher, A.; Yepes, G.; Hoffman, Y.; Gottlöber, S.; Catinella, B. The velocity function in the local environment from LCDM and LWDM constrained simulations. Astrophys. J.
**2009**, 700, 1779. [Google Scholar] [CrossRef] - Peebles, P.J.E.; Nusser, A. Nearby galaxies as pointers to a better theory of cosmic evolution. Nature
**2010**, 465, 565–569. [Google Scholar] [CrossRef] [Green Version] - Kormendy, J.; Drory, N.; Bender, R.; Cornell, M.E. Bulgeless Giant Galaxies Challenge Our Picture of Galaxy Formation by Hierarchical Clustering. Astrophys. J.
**2010**, 723, 54. [Google Scholar] [CrossRef] [Green Version] - Kormendy, J. Elliptical Galaxies and Bulges of Disc Galaxies: Summary of Progress and Outstanding Issues. In Galactic Bulges; Springer: Berlin/Heidelberg, Germany, 2016; pp. 431–477. [Google Scholar]
- Caramete, L.I.; Biermann, P.L. The catalog of nearby black hole candidates. arxiv
**2011**, arXiv:1107.2244. [Google Scholar] - Wang, F.; Yang, J.; Fan, X.; Hennawi, J.F.; Barth, A.J.; Banados, E.; Bian, F.; Boutsia, K.; Connor, T.; Davies, F.B.; et al. A Luminous Quasar at Redshift 7.642. Astrophys. J. Lett.
**2021**, 907, L1. [Google Scholar] [CrossRef] - de Vega, H.; Sanchez, N.G. Model independent analysis of dark matter points to a particle mass at the keV scale. Mon. Not. R. Astron. Soc.
**2010**, 404, 885. [Google Scholar] [CrossRef] [Green Version] - de Vega, H.; Salucci, P.; Sanchez, N.G. The mass of the dark matter particle from theory and observations. New Astron.
**2012**, 17, 653. [Google Scholar] [CrossRef] [Green Version] - de Vega, H.; Sanchez, N.G. Cosmological evolution of warm dark matter fluctuations. I. Efficient computational framework with Volterra integral equations. Phys. Rev. D
**2012**, 85, 043516. [Google Scholar] [CrossRef] [Green Version] - de Vega, H.; Sanchez, N.G. Cosmological evolution of warm dark matter fluctuations. II. Solution from small to large scales and keV sterile neutrinos. Phys. Rev. D
**2012**, 85, 043517. [Google Scholar] [CrossRef] [Green Version] - Destri, C.; de Vega, H.J.; Sanchez, N.G. Fermionic warm dark matter produces galaxy cores in the observed scales because of quantum mechanics. New Astron.
**2013**, 22, 39. [Google Scholar] [CrossRef] [Green Version] - Destri, C.; de Vega, H.J.; Sanchez, N.G. Quantum WDM fermions and gravitation determine the observed galaxy structures. Astropart. Phys.
**2013**, 46, 1. [Google Scholar] [CrossRef] [Green Version] - Destri, C.; de Vega, H.J.; Sanchez, N.G. Warm dark matter primordial spectra and the onset of structure formation at redshift z. Phys. Rev. D
**2013**, 88, 083512. [Google Scholar] [CrossRef] [Green Version] - de Vega, H.; Salucci, P.; Sanchez, N.G. Observational rotation curves and density profiles versus the Thomas–Fermi galaxy structure theory. Mon. Not. R. Astron. Soc.
**2014**, 442, 2717. [Google Scholar] [CrossRef] [Green Version] - Paduroiu, S.; Revaz, Y.; Pfenniger, D. Structure formation in warm dark matter cosmologies: Top-Bottom Upside-Down. arXiv
**2015**, arXiv:1506.03789. [Google Scholar] - Paduroiu, S. Structure Formation in Warm Dark Matter Cosmologies. Ph.D. Thesis, University of Geneva, Geneva, Switzerland, 2015. [Google Scholar]
- Sanchez, N.; Paduroiu, S.; Biermann, P.L. Warm Dark Matter Astrophysics in Agreement with Observations and keV Sterile Neutrinos: Synthesis of Highlights and Conclusions of the Chalonge -de Vega Meudon Workshop 2016 In Memoriam Héctor J. de Vega. 2016. Available online: https://hal.archives-ouvertes.fr/hal-01773092 (accessed on 16 October 2021).
- Macciò, A.V.; Stinson, G.; Brook, C.B.; Wadsley, J.; Couchman, H.M.P.; Shen, S.; Gibson, B.K.; Quinn, T. Halo Expansion in Cosmological Hydro Simulations: Toward a Baryonic Solution of the Cusp/Core Problem in Massive Spirals. Astrophys. J.
**2012**, 744, L9. [Google Scholar] [CrossRef] - Marinacci, F.; Pakmor, R.; Springel, V. The formation of disc galaxies in high-resolution moving-mesh cosmological simulations. Mon. Not. RAS
**2014**, 437, 1750. [Google Scholar] [CrossRef] - Gao, L.; Theuns, T. Lighting the Universe with filaments. Science
**2007**, 317, 1527. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Boyarsky, A.; Drewes, M.; Lasserre, T.; Mertens, S.; Ruchayskiy, O. Sterile Neutrino Dark Matter. Prog. Part. Nucl. Phys.
**2019**, 104, 1–45. [Google Scholar] [CrossRef] [Green Version] - Bode, P.; Ostriker, J.P.; Turok, N. Halo formation in warm dark matter models. Astrophys. J.
**2001**, 556, 93. [Google Scholar] [CrossRef] - Pierpaoli, E.; Borgani, S.; Masiero, A.; Yamaguchi, M. The Formation of Cosmic Structures in a Light Gravitino Dominated Universe. Phys. Rev. D
**1998**, 57, 2089. [Google Scholar] [CrossRef] [Green Version] - Alvarez-Gaumé, L.; Ginsparg, P.; Moore, G.; Vafa, C. An O(16) × O(16) heterotic string. Phys. Lett. B
**1986**, 171, 2. [Google Scholar] [CrossRef] - Dixon, L.G.; Harvey, J.A. String theories in ten dimensions without supersymmetry. Nucl. Phys. B
**1986**, 274, 18. [Google Scholar] [CrossRef] - Jedamzik, K.; Lemoine, M.; Moultaka, G. Gravitino dark matter in gauge mediated supersymmetry breaking. Phys. Rev. D
**2006**, 73, 1550. [Google Scholar] [CrossRef] [Green Version] - Gross, C.; Lebedev, O.; Mambrini, Y. Non-Abelian gauge fields as dark matter. J. High Energy Phys.
**2015**, 8, 158. [Google Scholar] [CrossRef] [Green Version] - McGuigan, M. Dark Horse, Dark Matter: Revisiting the SO(16)x SO(16)’ Nonsupersymmetric Model in the LHC and Dark Energy Era. arXiv
**2019**, arXiv:1907.01944. [Google Scholar] - Rios, M.; Marrani, A.; Chester, D. The Geometry of Exceptional Super Yang-Mills Theories. Phys. Rev. D
**2019**, 99, 046004. [Google Scholar] [CrossRef] [Green Version] - Rios, M.; Marrani, A.; Chester, D. Exceptional Super Yang-Mills in D = 27 + 3 and Worldvolume M-Theory. Phys. Lett. B
**2020**, 808, 135674. [Google Scholar] [CrossRef] - Dodelson, S.; Widrow, L.M. Sterile neutrinos as dark matter. Phys. Rev. Lett.
**1994**, 72, 17–20. [Google Scholar] [CrossRef] [Green Version] - Shi, X.; Fuller, G.M. New dark matter candidate: Nonthermal sterile neutrinos. Phys. Rev. Lett.
**1999**, 82, 2832. [Google Scholar] [CrossRef] [Green Version] - Dolgov, A.D. Neutrinos in cosmology. Phys. Rep.
**2002**, 370, 333. [Google Scholar] [CrossRef] [Green Version] - Asaka, T.; Shaposhnikov, M.; Kusenko, A. Opening a new window for warm dark matter. Phys. Lett. B
**2006**, 638, 401. [Google Scholar] [CrossRef] [Green Version] - Boyarsky, A.; Lesgourgues, J.; Ruchayskiy, O.; Viel, M. Realistic sterile neutrino dark matter with keV mass does not contradict cosmological bounds. Phys. Rev. Lett.
**2009**, 102, 201304. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Fuller, G.M.; Kishimoto, C.T.; Kusenko, A. Heavy sterile neutrinos, entropy and relativistic energy production, and the relic neutrino background. arXiv
**2011**, arXiv:1110.6479. [Google Scholar] - Lello, L.; Boyanovsky, D. Cosmological Implications of Light Sterile Neutrinos produced after the QCD Phase Transition. Phys. Rev. D
**2015**, 91, 063502. [Google Scholar] [CrossRef] [Green Version] - Paduroiu, S. Warm Dark Matter in Numerical Simulations. 2021; submitted to Universe, MDPI. [Google Scholar]
- Colombi, S.; Dodelson, S.; Widrow, L.M. Large Scale Structure Tests of Warm Dark Matter. Astrophys. J.
**1996**, 458, 1. [Google Scholar] [CrossRef] [Green Version] - Bezrukov, F.; Hettmansperger, H.; Lindner, M. keV sterile neutrino dark matter in gauge extensions of the standard model. Phys. Rev. D
**2010**, 81, 085032. [Google Scholar] [CrossRef] [Green Version] - Nemevšek, M.; Senjanović, G.; Zhang, Y. Warm dark matter in low scale left-right theory. J. Cosmol. Astropart. Phys.
**2012**, 7, 6. [Google Scholar] [CrossRef] [Green Version] - Patwardhan, A.V.; Fuller, G.M.; Kishimoto, C.T.; Kusenko, A. Diluted equilibrium sterile neutrino dark matter. Phys. Rev. D
**2015**, 92, 103509. [Google Scholar] [CrossRef] [Green Version] - Herms, J.; Ibarra, A.; Toma, T. A new mechanism of sterile neutrino dark matter production. JCAP
**2018**, 6, 36. [Google Scholar] [CrossRef] [Green Version] - Vafa, C. Evidence for F-Theory. Nucl. Phys. B
**1996**, 469, 403. [Google Scholar] [CrossRef] [Green Version] - Bars, I. S-theory. Phys. Rev. D
**1997**, 55, 2373. [Google Scholar] [CrossRef] [Green Version] - Bars, I. A case for 14 dimensions. Phys. Lett. B
**1997**, 403, 257. [Google Scholar] [CrossRef] [Green Version] - Sezgin, E. Super Yang-Mills in (11,3) Dimensions. Phys. Lett. B
**1997**, 403, 265. [Google Scholar] [CrossRef] [Green Version] - Nishino, H. Supersymmetric Yang-Mills Theories in D ⩾ 12. Nucl. Phys. B
**1998**, 523, 450. [Google Scholar] [CrossRef] [Green Version] - Rudychev, I.; Sezgin, E.; Sundell, P. Supersymmetry in dimensions beyond eleven. Nucl. Phys. Proc. Suppl.
**1998**, 68, 285. [Google Scholar] [CrossRef] [Green Version] - Witten, E. String Theory Dynamics In Various Dimensions. Nucl. Phys. B
**1995**, 443, 85. [Google Scholar] [CrossRef] [Green Version] - Banks, T.; Fischler, W.; Shenker, S.H.; Susskind, L. M Theory As A Matrix Model: A Conjecture. Phys. Rev. D
**1995**, 55, 5112. [Google Scholar] [CrossRef] [Green Version] - Truini, P.; Rios, M.; Marrani, A. The Magic Star of Exceptional Periodicity. In Proceedings of the 4th Mile High Conference on Nonassociative Mathematics, Denver, CO, USA, 29 July–5 August 2017. [Google Scholar]
- Truini, P.; Marrani, A.; Rios, M. Magic Star and Exceptional Periodicity: An approach to Quantum Gravity. In Proceedings of the 32nd International Colloquium on Group Theoretical Methods in Physics, Prague, Czech Republic, 9–13 July 2018. [Google Scholar]
- Marrani, A.; Truini, P.; Rios, M. The Magic of Being Exceptional. In Proceedings of the 32nd International Colloquium on Group Theoretical Methods in Physics, Prague, Czech Republic, 9–13 July 2018. [Google Scholar]
- de Wit, B.; Van Proeyen, A. Special geometry, cubic polynomials and homogeneous quaternionic spaces. Commun. Math. Phys.
**1992**, 149, 307. [Google Scholar] [CrossRef] [Green Version] - de Wit, B.; Vanderseypen, F.; Van Proeyen, A. Symmetry structure of special geometries. Nucl. Phys. B
**1993**, 400, 463. [Google Scholar] [CrossRef] [Green Version] - Reig, M.; Valle, J.W.F.; Vaquera-Araujo, C.A.; Wilczek, F. A Model of Comprehensive Unification. Phys. Lett. B
**2017**, 774, 667. [Google Scholar] [CrossRef] - BenTov, Y.; Zee, A. The Origin of Families and SO(18) Grand Unification. Phys. Rev. D
**2016**, 93, 065036. [Google Scholar] [CrossRef] [Green Version] - Vinberg, E.B. The theory of Convex Homogeneous Cones. In Transaction of the Moscow Mathematical Society for the Year 1963; American Mathematical Society: Providence, RI, USA, 1963; pp. 340–403. [Google Scholar]
- Alekseevsky, D.V.; Marrani, A.; Spiro, A. Special Vinberg Cones and the Entropy of BPS Extremal Black Holes. arXiv
**2021**, arXiv:2107.06797. [Google Scholar] [CrossRef] - Horava, P.; Witten, E. Heterotic and Type I String Dynamics from Eleven Dimensions. Nucl. Phys. B
**1996**, 460, 506. [Google Scholar] [CrossRef] [Green Version] - Horava, P.; Witten, E. Eleven-Dimensional Supergravity on a Manifold with Boundary. Nucl. Phys. B
**1996**, 475, 94. [Google Scholar] [CrossRef] [Green Version] - Horowitz, G.; Susskind, L. Bosonic M Theory. J. Math. Phys.
**2001**, 42, 3152–3160. [Google Scholar] [CrossRef] - Watabiki, Y. The bosonic string and superstring models in 26 + 2 and 10 + 2 dimensional space–time, and the generalized Chern-Simons action. J. High Energy Phys.
**2003**, 5, 1. [Google Scholar] [CrossRef] [Green Version] - Jungman, G.; Kamionkowski, M.; Griest, K. Supersymmetric Dark Matter. Phys. Rept.
**1996**, 267, 195. [Google Scholar] [CrossRef] [Green Version] - ATLAS Collaboration. Search for bottom-squark pair production with the ATLAS detector in final states containing Higgs bosons, bb-jets and missing transverse momentum. J. High Energy Phys.
**2019**, 12, 60. [Google Scholar] - Duff, M.J.; Inami, T.; Pope, C.N.; Sezgin, E.; Stelle, K.S. Semiclassical quantization of the supermembrane. Nucl. Phys. B
**1988**, 297, 515. [Google Scholar] [CrossRef] [Green Version] - Cederwall, M.; von Gussich, A.; Nilsson, B.E.W.; Westerberg, A. The Dirichlet super three-brane in ten-dimensional type IIB supergravity. Nucl. Phys. B
**1997**, 490, 163–178. [Google Scholar] [CrossRef] [Green Version] - Heckman, J.J.; Vafa, C. From F-theory GUTs to the LHC. arXiv
**2008**, arXiv:hep-th/0809.3452. [Google Scholar] - Randall, L.; Sundrum, R. A Large mass hierarchy from a small extra dimension. Phys. Rev. Lett.
**1999**, 83, 3370–3373. [Google Scholar] [CrossRef] [Green Version] - Hirayama, T. A Holographic dual of CFT with flavor on de Sitter space. J. High Energy Phys.
**2006**, 6, 13. [Google Scholar] [CrossRef] [Green Version] - Cheung, C.; Remmen, G.N. Twofold Symmetries of the Pure Gravity Action. J. High Energy Phys.
**2017**, 1, 104. [Google Scholar] [CrossRef] - MacDowell, S.W.; Mansouri, F. Unified geometric theory of gravity and supergravity. Phys. Rev. Lett.
**1977**, 38, 739–742. [Google Scholar] [CrossRef] - Gürsey, F.; Ramond, P.; Sikivie, P.A. Universal Gauge Theory Model Based on E6. Phys. Lett. B
**1976**, 60, 177–180. [Google Scholar] [CrossRef] - Boyle, L. The Standard Model, The Exceptional Jordan Algebra, and Triality. arXiv
**2006**, arXiv:2006.16265. [Google Scholar] - Bars, I.; Günaydin, M. Grand Unification with the Exceptional Group E8. Phys. Rev. Lett.
**1980**, 45, 859. [Google Scholar] [CrossRef] - Marrani, A.; Rios, M.; Chester, D. Monstrous M-theory. arXiv
**2008**, arXiv:hep-th/2008.06742. [Google Scholar] - Gaberdiel, M.R.; West, P.C. Kac-Moody algebras in perturbative string theory. J. High Energy Phys.
**2002**, 8, 49. [Google Scholar] [CrossRef] [Green Version] - Kostant, B. The Principle of Triality and A Distinguished Unitary Representation of SO(4,4). In Differential Geometrical Methods in Theoretical Physics; Bleuler, K., Werner, M., Eds.; NATO ASI Series (Series C: Mathematical and Physical Sciences); Springer: Dordrecht, The Netherlands, 1988; Volume 250. [Google Scholar]
- Chester, D.; Marrani, A.; Rios, M. Beyond the standard model with six-dimensional spacetime. arXiv
**2020**, arXiv:2002.02391. [Google Scholar] - Aldazabal, G.; Ibanez, L.E.; Quevedo, F.; Uranga, A.M. D-Branes at Singularities: A Bottom-Up Approach to the String Embedding of the Standard Model. J. High Energy Phys.
**2000**, 8, 2. [Google Scholar] [CrossRef] [Green Version] - Martinec, E.J. Geometrical structures of M theory. arXiv
**1996**, arXiv:hep-th/9608017. [Google Scholar] - Krasnov, K. Spin(11,3), particles and octonions. arXiv
**2021**, arXiv:hep-th/2104.01786. [Google Scholar] - Slansky, R. Group Theory for Unified Model Building. Phys. Rept.
**1981**, 79, 1–28. [Google Scholar] [CrossRef]

**Figure 1.**A Magic Star-type projection of ${\mathfrak{e}}_{8(-24)}^{\left(1\right)}$ that contains ${\mathfrak{e}}_{6(-26)}^{\left(1\right)}$ in the center, named after the star polygon geometric shape.

**Figure 2.**The intersections of branes in $D=27+3$. For instance, the 3-brane is dual to the 23-brane, which contains the 7-brane and 15-brane.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Paduroiu, S.; Rios, M.; Marrani, A.; Chester, D.
Warm Dark Matter from Higher-Dimensional Gauge Theories. *Universe* **2021**, *7*, 462.
https://doi.org/10.3390/universe7120462

**AMA Style**

Paduroiu S, Rios M, Marrani A, Chester D.
Warm Dark Matter from Higher-Dimensional Gauge Theories. *Universe*. 2021; 7(12):462.
https://doi.org/10.3390/universe7120462

**Chicago/Turabian Style**

Paduroiu, Sinziana, Michael Rios, Alessio Marrani, and David Chester.
2021. "Warm Dark Matter from Higher-Dimensional Gauge Theories" *Universe* 7, no. 12: 462.
https://doi.org/10.3390/universe7120462