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We propose matter wavefunctions on resolutions of $T^2/mathbb{Z}_N$ singularities with constant magnetic fluxes. In the blow-down limit, the obtained wavefunctions of chiral zero-modes result in those on the magnetized $T^2/mathbb{Z}_N$ orbifold models, but the wavefunctions of $mathbb{Z}_N$-invariant zero-modes receive the blow-up effects around fixed points of $T^2/mathbb{Z}_N$ orbifolds. Such blow-up effects change the selection rules and Yukawa couplings among the chiral zero-modes as well as the modular symmetry, in contrast to those on the magnetized $T^2/mathbb{Z}_N$ orbifold models.
We investigate chiral zero modes and winding numbers at fixed points on $T^2/mathbb{Z}_N$ orbifolds. It is shown that the Atiyah-Singer index theorem for the chiral zero modes leads to a formula $n_+-n_-=(-V_++V_-)/2N$, where $n_{pm}$ are the numbers
Generalizations of the AGT correspondence between 4D $mathcal{N}=2$ $SU(2)$ supersymmetric gauge theory on ${mathbb {C}}^2$ with $Omega$-deformation and 2D Liouville conformal field theory include a correspondence between 4D $mathcal{N}=2$ $SU(N)$ su
We discuss an effective way for analyzing the system on the magnetized twisted orbifolds in operator formalism, especially in the complicated cases $T^{2}/Z_{3}$, $T^{2}/Z_{4}$ and $T^{2}/Z_{6}$. We can obtain the exact and analytical results which c
The incorporation of Wilson lines leads to an extension of the modular symmetries of string compactification beyond $mathrm{SL}(2,mathbb Z)$. In the simplest case with one Wilson line $Z$, Kahler modulus $T$ and complex structure modulus $U$, we are
The $mathbb{Z}_2times mathbb{Z}_2$ heterotic string orbifold yielded a large space of phenomenological three generation models and serves as a testing ground to explore how the Standard Model of particle physics may be incorporated in a theory of qua