Revisiting modular symmetry in magnetized torus and orbifold compactifications
Abstract
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 Γ ≡S L (2 ,Z ) , Γ ∼ ≡S L ∼ (2 ,Z ) . Each wave function on T2 with the magnetic flux M transforms under Γ ∼ (2 |M |) , which is the normal subgroup of S L ∼ (2 ,Z ) . Then, |M | zero modes are representations of the quotient group Γ∼2 |M | '≡Γ ∼ /Γ ∼ (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.
- Publication:
-
Physical Review D
- Pub Date:
- November 2020
- DOI:
- 10.1103/PhysRevD.102.105010
- arXiv:
- arXiv:2005.12642
- Bibcode:
- 2020PhRvD.102j5010K
- Keywords:
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- High Energy Physics - Theory;
- High Energy Physics - Phenomenology;
- Mathematics - Number Theory
- E-Print:
- 29 pages