Realizing three generations of the Standard Model fermions in the type IIB matrix model

Abstract

We discuss how the Standard Model particles appear from the type IIB matrix model, which is considered to be a nonperturbative formulation of superstring theory. In particular, we are concerned with a constructive definition of the theory, in which we start with finite-N matrices and take the large-N limit afterwards. In that case, it was pointed out recently that realizing chiral fermions in the model is more difficult than it had been thought from formal arguments at N=infinity and that introduction of a matrix version of the warp factor is necessary. Based on this new insight, we show that two generations of the Standard Model fermions can be realized by considering a rather generic configuration of fuzzy S^2 and fuzzy S^2 * S^2 in the extra dimensions. We also show that three generations can be obtained by squashing one of the S^2's that appear in the configuration. Chiral fermions appear at the intersections of the fuzzy manifolds with nontrivial Yukawa couplings to the Higgs field, which can be calculated from the overlap of their wave functions.

28 pages, 11 figures; (v2) references added, typos corrected; (v3) footnote added, version to be published on JHEP

References in corpus (1)

• Orbifolds, fuzzy spheres and chiral fermions

Cited by in corpus (15)

• Complex Langevin analysis of the space-time structure in the Lorentzian type IIB matrix model
• Covariant cosmological quantum space-time, higher-spin and gravity in the IKKT matrix model
• On the quantum structure of space-time, gravity, and higher spin in matrix models
• Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model
• Self-intersecting fuzzy extra dimensions from squashed coadjoint orbits in $\mathcal{N}=4$ SYM and matrix models
• Higher-spin gravity and torsion on quantized space-time in matrix models
• Lorentzian Fuzzy Spheres
• Complex Langevin analysis of the spontaneous breaking of 10D rotational symmetry in the Euclidean IKKT matrix model
• Quantum (Matrix) Geometry and Quasi-Coherent States
• 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
• A Scaling Relation, $Z_m$-type Deconfinement Phases and Imaginary Chemical Potentials in Finite Temperature Large-$N$ Gauge Theories
• Matrix model and Yukawa couplings on the noncommutative torus