Abstract
We study the modular symmetry on magnetized toroidal orbifolds with Scherk-Schwarz phases. In particular, we investigate finite modular flavor groups for three-generation modes on magnetized orbifolds. The three-generation modes can be the three-dimensional irreducible representations of covering groups and central extended groups of ${\mathrm{\ensuremath{\Gamma}}}_{N}$ for $N=3$, 4, 5, 7, 8, 16, that is, covering groups of $\mathrm{\ensuremath{\Delta}}(6(N/2{)}^{2})$ for $N=\mathrm{even}$ and central extensions of $PSL(2,{\mathbb{Z}}_{N})$ for $N=\mathrm{odd}$ with Scherk-Schwarz phases. We also study anomaly behaviors.
Highlights
The origin of the flavor structure, such as quark and lepton masses and their mixing angles, is one of the most significant mysteries in particle physics
We study modular flavor groups of the three-generation modes on magnetized orbifolds
The modular symmetry is broken in wave functions for odd magnetic fluxes and vanishing Wilson lines and SS phases, but the modular symmetry remains for odd magnetic fluxes and nonvanishing WLs, which is a discrete shift of the coordinate
Summary
The origin of the flavor structure, such as quark and lepton masses and their mixing angles, is one of the most significant mysteries in particle physics. We find that the three-generation modes are the three-dimensional representations of corresponding covering groups and central extended groups of the above finite modular subgroups provided in Ref. The modular symmetry is broken in wave functions for odd magnetic fluxes and vanishing Wilson lines and SS phases, but the modular symmetry remains for odd magnetic fluxes and nonvanishing WLs, which is a discrete shift of the coordinate We find that the three-generation modes are the three-dimensional representations of the quadruple covering groups and Z8 central extended groups of the corresponding modular flavor groups provided in Ref. In Appendix D we express the three-dimensional modular forms obtained from the wave functions on magnetized orbifolds
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
