Modular symmetry and zeros in magnetic compactifications

A bstract We discuss the modular symmetry and zeros of zero-mode wave functions on two-dimensional torus T 2 and toroidal orbifolds T 2 / ℤ N ( N = 2 , 3 , 4 , 6) with a background homogeneous magnetic field. As is well-known, magnetic flux contributes to the index in the Atiyah-Singer index theorem...

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Bibliographic Details
Published in:The journal of high energy physics 2021-10, Vol.2021 (10), p.1-22, Article 54
Main Author: Tatsuta, Yoshiyuki
Format: Article
Language:English
Subjects:
Boundary conditions
Classical and Quantum Gravitation
Electrons
Elementary Particles
Field Theories in Higher Dimensions
Global Symmetries
High energy physics
Magnetic flux
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
String Theory
Symmetry
Toruses
Wave functions
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Summary:A bstract We discuss the modular symmetry and zeros of zero-mode wave functions on two-dimensional torus T 2 and toroidal orbifolds T 2 / ℤ N ( N = 2 , 3 , 4 , 6) with a background homogeneous magnetic field. As is well-known, magnetic flux contributes to the index in the Atiyah-Singer index theorem. The zeros in magnetic compactifications therefore play an important role, as investigated in a series of recent papers. Focusing on the zeros and their positions, we study what type of boundary conditions must be satisfied by the zero modes after the modular transformation. The consideration in this paper justifies that the boundary conditions are common before and after the modular transformation.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP10(2021)054