Magnetized twisted orbifold models for the origin of generation and chirality

Abstract

The Standard Model (SM) is ompleted by the disovery of the Higgs partile and the measurement of its mass. The SM has ahieved great suesses for explaining many experimental results, e.g., non-zero gauge boson masses, suppression of avor hanging neutral urrents, and CP-violating proesses. However, there are some puzzles whih are not explained in the SM as follows: The origin of the generation, the hiral struture, the mass hierarhy of the matters, the gauge struture, and the gravitational interation. In this thesis, we fous on former four puzzles and investigate models whih an solve them. One of the attrative ideas for suh model-building is higher-dimensional eld theory where the dimension of the spae-time is more than four. We obtain four-dimensional (4D) eetive eld theory by performing dimensional redution. The advantages of this senario are the follows: First, the 4D salar eld arises from higher-dimensional vetor eld. Seond, hierarhial Yukawa ouplings may be obtained by overlap integrals of extra-dimensional wavefuntions. In addition to higher-dimensional theory, toroidal ompatiation with onstant magneti ux is useful for solving some of the puzzles whih are mentioned in the above. On this bakground, we an solve the zero-mode equation of Kaluza{Klein modes analytially. This analytiity helps us to perform overlap integrals and to ompute the Yukawa ouplings in the eetive theory. Furthermore, we obtain the solution whih is hiral and degenerate. Thanks to these properties of the solution, three generations of hiral fermions an be realized in the eetive theory. We also onsider the twisted orbifolding. This is useful for realizing atual avor struture as well as for pro jeting out exoti partiles. We analyze the system on magnetized twisted orbifold T2 =ZN (N = 2; 3; 4; 6) by using the operator formalism and investigate the number of independent zero-modes on the orbifold for eah ZN eigenvalues. Based on these aspets, we propose the ten-dimensional (10D) super Yang{Mills (SYM) theory on magnetized twisted orbifolds as a framework for solving the puzzles in the SM. 10D SYM is a well-motivated higher-dimensional theory sine this appears as low-energy limit of some types of superstring theories.Ginger It! By using the results obtained by the above investigation, we lassify all the possible ongurations of the parameters whih realize three generations of hiral fermions in 4D eetive theory. This lassiation is a rst step for building realisti models with three generations, hiral fermions, and hierarhial Yukawa ouplings.