Modular symmetry and zeros in magnetic compactifications

Modular symmetry and zeros in magnetic compactifications

Abstract 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...

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Main Author: Yoshiyuki Tatsuta
Format: Article
Language:English
Published: SpringerOpen 2021-10-01
Series:Journal of High Energy Physics
Subjects:
Field Theories in Higher Dimensions
Global Symmetries
Online Access:https://doi.org/10.1007/JHEP10(2021)054
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spelling doaj-4e77ed9778474a86b3faeb73200e0ac12021-10-10T11:52:25ZengSpringerOpenJournal of High Energy Physics1029-84792021-10-0120211012210.1007/JHEP10(2021)054Modular symmetry and zeros in magnetic compactificationsYoshiyuki Tatsuta0Scuola Normale Superiore and INFNAbstract 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.https://doi.org/10.1007/JHEP10(2021)054Field Theories in Higher DimensionsGlobal Symmetries
collection DOAJ
language English
format Article
sources DOAJ
author Yoshiyuki Tatsuta
spellingShingle Yoshiyuki Tatsuta
Modular symmetry and zeros in magnetic compactifications
Journal of High Energy Physics
Field Theories in Higher Dimensions
Global Symmetries
author_facet Yoshiyuki Tatsuta
author_sort Yoshiyuki Tatsuta
title Modular symmetry and zeros in magnetic compactifications
title_short Modular symmetry and zeros in magnetic compactifications
title_full Modular symmetry and zeros in magnetic compactifications
title_fullStr Modular symmetry and zeros in magnetic compactifications
title_full_unstemmed Modular symmetry and zeros in magnetic compactifications
title_sort modular symmetry and zeros in magnetic compactifications
publisher SpringerOpen
series Journal of High Energy Physics
issn 1029-8479
publishDate 2021-10-01
description Abstract 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.
topic Field Theories in Higher Dimensions
Global Symmetries
url https://doi.org/10.1007/JHEP10(2021)054
work_keys_str_mv AT yoshiyukitatsuta modularsymmetryandzerosinmagneticcompactifications
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