2020/05/31 by Shota Kikuchi, Tatsuo Kobayashi, Shintaro Takada +2
Computer Science · Mathematics · Physics and Astronomy · #Algorithms and Data Compression #Black Holes and Theoretical Physics #Computer science #Geometry #Mathematics #Modular design #Noncommutative and Quantum Gravity Theories #Orbifold #Physics #Symmetry (geometry) #Theoretical physics #Torus #hep-ph #hep-th #math.NT
paper · pdf · doi:10.1103/physrevd.102.105010
published as Phys. Rev. D 102, 105010 (2020) · 29 pages
arxiv created 2020/11/07 · openalex publication_date 2020/11/09 · arxiv updated 2020/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the modular symmetry in T2 and orbifold comfactifications with magnetic fluxes. There are |M| zero modes on T2 with the magnetic flux M. Their wave functions as well as massive modes behave as modular forms of weight 1/2 and represent the double covering group of \mathrm\ensuremathΓ\ensuremath≡SL(2,ℤ), \stackrel\texttildelow\mathrm\ensuremathΓ\ensuremath≡\stackrel\texttildelowSL(2,ℤ). Each wave function on T2 with the magnetic flux M transforms under \stackrel\texttildelow\mathrm\ensuremathΓ(2|M|), which is the normal subgroup of \stackrel\texttildelowSL(2,ℤ). Then, |M| zero modes are representations of the quotient group \stackrel\texttildelow\mathrm\ensuremathΓ2|M|^\ensuremath'\ensuremath≡\stackrel\texttildelow\mathrm\ensuremathΓ/\stackrel\texttildelow\mathrm\ensuremathΓ(2|M|). We also study the modular symmetry on twisted and shifted orbifolds T2/ℤN. Wave functions are decomposed into smaller representations by eigenvalues of twist and shift. They provide us with reduction of reducible representations on T2.