An extended standard model and its Higgs geometry from the matrix model

Abstract

We find a simple brane configuration in the IKKT matrix model which resembles the standard model at low energies, with a second Higgs doublet and right-handed neutrinos. The electroweak sector is realized geometrically in terms of two minimal fuzzy ellipsoids, which can be interpreted in terms of four point-branes in the extra dimensions. The electroweak Higgs connects these branes and is an indispensable part of the geometry. Fermionic would-be zero modes arise at the intersections with two larger branes, leading precisely to the correct chiral matter fields at low energy, along with right-handed neutrinos which can acquire a Majorana mass due to a Higgs singlet. The larger branes give rise to $SU(3{)}_c$, extended by $U(1{)}_B$ and another $U(1)$ which are anomalous at low energies and expected to disappear. At higher energies, mirror fermions and additional fields arise, completing the full $\mathcal{N}=4$ supersymmetry. The brane configuration is a solution of the model, assuming a suitable effective potential and a non-linear stabilization of the singlet Higgs. The basic results can be carried over to $\mathcal{N}=4$ $SU(N)$ super-Yang-Mills on ordinary Minkowski space with sufficiently large $N$.

41 pages, 8 figures V2: rotating background replaced by static one, stabilized by a potential. References added. V3: minor corrections and improved discussion, published version

References in corpus (3)

• Progress in D-brane model building
• Curvature and Gravity Actions for Matrix Models II: the case of general Poisson structure
• Stueckelberg Axions and Anomalous Abelian Extensions of the Standard Model

Cited by in corpus (13)

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• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• Spinning squashed extra dimensions and chiral gauge theory from $\mathcal{N}=4$ SYM
• The emergence of expanding space-time and intersecting D-branes from classical solutions in the Lorentzian type IIB matrix model
• On the structure of the emergent 3d expanding space in the Lorentzian type IIB matrix model
• Intersecting branes, Higgs sector, and chirality from $\mathcal{N}=4$ SYM with soft SUSY breaking
• Aspects of perturbative quantum field theory on non-commutative spaces
• Matrix model and Yukawa couplings on the noncommutative torus
• Chiral low-energy physics from squashed branes in deformed $\mathcal{N}=4$ SYM
• A general procedure to find ground state solutions for finite $N$ M(atrix) theory. Reduced models and SUSY quantum cosmology