Magnetized orbifolds and localized flux

Abstract

Magnetized orbifolds play an important role in compactifications of string theories and higher-dimensional field theories to four dimensions. Magnetic flux leads to chiral fermions, it can be a source of supersymmetry breaking and it is an important ingredient of moduli stabilization. Flux quantization on orbifolds is subtle due to the orbifold singularities. Generically, Wilson line integrals around these singularities are non-trivial, which can be interpreted as localized flux. As a consequence, flux densities on orbifolds can take the same values as on tori. We determine the transition functions for the flux vector bundle on the orbifold $T^2/{\mathbb{Z}}_2$ and the related twisted boundary conditions of zero-mode wave functions. We also construct "untwisted" zero-mode functions that are obtained for singular vector fields related to the Green's function on a torus, and we discuss the connection between zeros of the wave functions and localized flux. Twisted and untwisted zero-mode functions are related by a singular gauge transformation.

36 pages, 13 figures, 2 tables

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Cited by in corpus (7)

• Loop Fayet-Iliopoulos terms in $T^2/Z_2$ models: instability and moduli stabilization
• Zero-mode counting formula and zeros in orbifold compactifications
• Index theorem on magnetized blow-up manifold of $T^2/{\mathbb{Z}}_N$
• Remark on modular weights in low-energy effective field theory from type II string theory
• Index theorem on $T^2/{\mathbb{Z}}_N$ orbifolds
• Modular symmetry and zeros in magnetic compactifications
• Wavefunctions on $S^2$ with flux and branes