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 byU(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 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 N = 4 SU(N) super Yang-Mills on ordinary Minkowski space with sufficiently large N.© The Author(s) 2014.