Related papers: Zero-mode counting formula and zeros in orbifold c…
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…
We analyze the number of independent chiral zero modes and the winding numbers at the fixed points on $T^2/{\mathbb{Z}}_N$ ($N=2,3,4,6$) orbifolds with magnetic flux. In the case of $N=2$, we derive the index formula…
We investigate blow-up manifolds of $T^2/{\mathbb{Z}}_N\,(N=2,3,4,6)$ orbifolds with magnetic flux $M$. Since the blow-up manifolds have no singularities, we can apply the Atiyah-Singer index theorem to them. Then, we establish the…
We discuss the modular symmetry and zeros of zero-mode wave functions on two-dimensional torus $T^2$ and toroidal orbifolds $T^2/\mathbb{Z}_N$ ($N=2,3,4,6$) with a background homogeneous magnetic field. As is well-known, magnetic flux…
We investigate the independent chiral zero modes on the orbifolds from the Atiyah-Segal-Singer fixed point theorem. The required information for this calculation includes the fixed points of the orbifold and the manner in which the spatial…
We study $T^2/Z_N$ orbifold models with magnetic fluxes. We propose a systematic way to analyze the number of zero-modes and their wavefunctions by use of modular transformation. Our results are consistent with the previous results, and our…
We study fermion zero-mode wavefunctions on $T^4/Z_N$ orbifold with background magnetic fluxes. The number of zero-modes is analyzed by use of $Sp(4,\mathbb{Z})$ modular transformation. Conditions needed to realize three generation models…
A counting formula for computing the number of (Majorana) zero modes bound to topological point defects is evaluated in a gradient expansion for systems with charge-conjugation symmetry. This semi-classical counting of zero modes is applied…
We study chiral zero-mode wave functions on blow-up manifolds of $T^2/Z_N$ orbifolds with both bulk and localized magnetic flux backgrounds. We introduce a singular gauge transformation in order to remove $Z_N$ phases for $Z_N$ twisted…
We propose new backgrounds of extra dimensions to lead to four-dimensional chiral models with three generations of matter fermions, that is $T^2/Z_N$ twisted orbifolds with magnetic fluxes. We consider gauge theory on six-dimensional…
We consider a six dimensional gauge theory compactified on $T^2/\mathbb{Z}_2$ with magnetic flux. The configurations of models are classified by winding numbers at the fixed points. Requiring the existence of generation numbers and Yukawa…
This thesis contains an introductory chapter on orbifolds. The following chapter explains the foundations of orientifolds. Chapters 4-7 present own research. In chapter 4 we quantize open strings with linear boundary conditions, as they…
We study the modular symmetry of zero-modes on $T_1^2 \times T_2^2$ and orbifold compactifications with magnetic fluxes, $M_1,M_2$, where modulus parameters are identified. This identification breaks the modular symmetry of $T^2_1 \times…
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…
Recently, the connection between Majorana fermions bound to defects in arbitrary dimensions, and complex momentum roots of the vanishing determinant of the corresponding bulk Bogoliubov-de Gennes (BdG) Hamiltonian, has been established…
We study the modular symmetry in $T^2$ and orbifold comfactifications with magnetic fluxes. There are $|M|$ zero-modes on $T^2$ with the magnetic flux $M$. Their wavefunctions as well as massive modes behave as modular forms of weight $1/2$…
M(atrix) theory compactified on an orbifold ${\bf T}_9/{\bf Z}_2$ is studied. Via zero-brane parton scattering we find that each of the $2^9 = 512$ orbifold fixed points carry $-1/32$ units of zero-brane charge. The anomalous flux is…
We study warped compactifications to three dimensions, realized as an orientifold of type IIA string theory on T^7. By turning on 3- and 4-form fluxes on the torus in a supersymmetric way, we generate a potential for the moduli fields. We…
We consider a toroidal configuration of cosmic string in 3+1 dimensions in an abelian Higgs model, a compactification of the Nielsen-Olesen string. This object is classically unstable. We explicitly compute the number of permitted zero…
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 $T^2/\mathbb{Z}_N$…