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.
Highlights
Dynamics such as confinement of quarks, which can never be understood in perturbation theory
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 this paper we discussed how the Standard Model appears from the type IIB matrix model
Summary
Where ΓM are 32 × 32 gamma matrices in 10d. The bosonic N × N matrices AM (M = 0, . . . , 9) are traceless Hermitian, while the fermionic N × N matrices Ψα (α = 1, . . . , 32) are Majorana-Weyl fermions in 10d, and, in particular, they satisfy. [28] concerning the appearance of chiral fermions in 4d from the type IIB matrix model In this model, the space-time is represented by the ten bosonic N × N Hermitian matrices AM I = 6 corresponds to the point (x4, x5, x6) = (0, 1, 1) on the fuzzy S2 (3.4), whereas j = 6 corresponds to the point (x5, x6, x7) = (1, 1, 0) and (x4, x8, x9) = (0, 0, 0) on the fuzzy S2 × S2 (3.5) This implies that the wave function of the right-handed chiral mode is localized at one of the intersection points (x5, x6) = (1, 1) in figure 1. The wave function of the right-handed chiral mode is quite different from (3.10), and it does not satisfy (2.23) generically. We can obtain a single chiral zero mode in four dimensions
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