Abstract
We apply our formalism for supersymmetric theories in the context of noncommutative geometry to explore the existence of a noncommutative version of the minimal supersymmetric Standard Model (MSSM). We obtain the exact particle content of the MSSM and identify (in form) its interactions, but conclude that their coefficients are such that the standard action functional used in noncommutative geometry is in fact not supersymmetric.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Keep in mind that we ensure the Hilbert space being complex by defining it as a bimodule of the complexification \(\mathscr {A}^{\mathbb {C}}\) of \(\mathscr {A}\), rather than of \(\mathscr {A}\) itself [3].
- 2.
In the strict sense the Standard Model does not feature a right handed neutrino (nor does the MSSM), but allows for extensions that do. On the other hand the more recent derivations of the SM from noncommutative geometry naturally come with a right-handed neutrino. We will incorporate it from the outset, always having the possibility to discard it should we need to.
References
T. van den Broek, W.D. van Suijlekom, Going beyond the standard model with noncommutative geometry. J. High Energy Phys. 3, 112 (2013)
A.H. Chamseddine, A. Connes, The spectral action principle. Commun. Math. Phys. 186, 731–750 (1997)
A.H. Chamseddine, A. Connes, Why the standard model. J. Geom. Phys. 58, 38–47 (2008)
A.H. Chamseddine, A. Connes, M. Marcolli, Gravity and the standard model with neutrino mixing. Adv. Theor. Math. Phys. 11, 991–1089 (2007)
D.J.H. Chung, L.L. Everett, G.L. Kane, S.F. King, J. Lykken, L.T. Wang, The soft supersymmetry-breaking Lagrangian: theory and applications. Phys. Rep. 407, 1–203 (2005)
A. Connes, Noncommutative Geometry (Academic Press, Boston, 1994)
A. Connes, Gravity coupled with matter and the foundation of noncommutative geometry. Commun. Math. Phys. 182, 155–176 (1996)
A. Connes, Noncommutative Geometry Year 2000 (2007), math/0011193
M. Drees, R. Godbole, P. Roy, Theory and Phenomenology of Sparticles (World Scientific Publishing Co., Singapore, 2004)
K. van den Dungen, W.D. van Suijlekom, Electrodynamics from noncommutative geometry. J. Noncommutative Geom. 7, 433–456 (2013)
P.B. Gilkey, Invariance Theory, the Heat Equation and the Atiyah-Singer Index Theorem, vol. 11, Mathematics Lecture Series (Publish or Perish, Wilmington, 1984)
B. Iochum, T. Schücker, C. Stephan, On a classification of irreducible almost commutative geometries. J. Math. Phys. 45, 5003–5041 (2004)
T. Krajewski, Classification of finite spectral triples. J. Geom. Phys. 28, 1–30 (1998)
F. Lizzi, G. Mangano, G. Miele, G. Sparano, Fermion Hilbert space and fermion doubling in the noncommutative geometry approach to gauge theories. Phys. Rev. D 55, 6357–6366 (1997)
T. Schücker, Spin Group and Almost Commutative Geometry (2007), hep-th/0007047
J.C. Várilly, An Introduction to Noncommutative Geometry (European Mathematical Society, Zurich, 2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 The Author(s)
About this chapter
Cite this chapter
Beenakker, W., van den Broek, T., van Suijlekom, W.D. (2016). The Noncommutative Supersymmetric Standard Model. In: Supersymmetry and Noncommutative Geometry. SpringerBriefs in Mathematical Physics, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-319-24798-4_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-24798-4_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-24796-0
Online ISBN: 978-3-319-24798-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)