2021/02/12 by Gui-Jun Ding, Ferruccio Feruglio, Xiang-Gan Liu · 54 citations
Materials Science · Physics and Astronomy · #Black Holes and Theoretical Physics #Discrete symmetry #Invariant (physics) #Modular design #Moduli #Moduli space #Observable #Quantum Mechanics and Non-Hermitian Physics #Quasicrystal Structures and Properties #Symmetry (geometry) #Symplectic geometry #hep-ph #hep-th
paper · pdf · doi:10.21468/scipostphys.10.6.133
published in SciPost Physics 10(6) (SciPost.org) · 37 pages, 2 figures
arxiv created 2021/02/12 · openalex created_date 2021/03/01 · openalex publication_date 2021/06/07 · arxiv updated 2021/06/09 · openalex updated_date 2026/08/05
We analyze CP symmetry in symplectic modular-invariant supersymmetric theories. We show that for genus g≥ 3 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> the definition of CP is unique, while two independent possibilities are allowed when g≤ 2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> . We discuss the transformation properties of moduli, matter multiplets and modular forms in the Siegel upper half plane, as well as in invariant subspaces. We identify CP-conserving surfaces in the fundamental domain of moduli space. We make use of all these elements to build a CP and symplectic invariant model of lepton masses and mixing angles, where known data are well reproduced and observable phases are predicted in terms of a minimum number of parameters.