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Register a new userResolved Toroidal Orbifolds and their Orientifolds
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We discuss the resolution of toroidal orbifolds. For the resulting smooth Calabi-Yau manifolds, we calculate the intersection ring and determine the divisor topologies. In a next step, the orientifold quotients are constructed.
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The aim of this paper is to study orientifolds of c=1 conformal field theories. A systematic analysis of the allowed orientifold projections for c=1 orbifold conformal field theories is given. We compare the Klein bottle amplitudes obtained at rational points with the orientifold projections that we claim to be consistent for any value of the orbifold radius. We show that the recently obtained Klein bottle amplitudes corresponding to exceptional modular invariants, describing bosonic string theories at fractional square radius, are also in agreement with those orientifold projections.
A classification of D-branes in Type IIB Op^- orientifolds and orbifolds in terms of Real and equivariant KK-groups is given. We classify D-branes intersecting orientifold planes from which are recovered some special limits as the spectrum for D-branes on top of Type I Op^- orientifold and the bivariant classification of Type I D-branes. The gauge group and transformation properties of the low energy effective field theory living in the corresponding unstable D-brane system are computed by extensive use of Clifford algebras. Some speculations about the existence of oth
We study the CP-violating phase of the quark sector in the $U(8)$ flavor model on $T^2/Z_N , (N=2,3,4,6)$ with non-vanishing magnetic fluxes, where properties of possible origins of the CP violation are investigated minutely. In this system, a non-vanishing value is mandatory in the real part of the complex modulus parameter $tau$ of the two-dimensional torus. On $T^2$ without orbifolding, underlying discrete flavor symmetries severely restrict the form of Yukawa couplings and it is very difficult to reproduce the observed pattern in the quark sector including the CP-violating phase $delta_{rm CP}$. In cases of multiple Higgs doublets emerging on $T^2/Z_2$, the mass matrices of the zero-mode fermions can be written in the Gaussian textures by choosing appropriate configurations of vacuum expectation values of the Higgs fields. When such Gaussian textures of mass matrices are realized, we show that all of the quark profiles, which are mass hierarchies among the quarks, quark mixing angles, and $delta_{rm CP}$ can be simultaneously realized.
Following on from a general observation in an earlier paper, we consider the continuous symmetries of a certain class of conformal field theories constructed from lattices and their reflection-twisted orbifolds. It is shown that the naive expectation that the only such (inner) symmetries are generated by the modes of the vertex operators corresponding to the states of unit conformal weight obtains, and a criterion for this expectation to hold in general is proposed.
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 led to the Siegel modular group $mathrm{Sp}(4,mathbb Z)$. It includes $mathrm{SL}(2,mathbb Z)_Ttimesmathrm{SL}(2,mathbb Z)_U$ as well as $mathbb Z_2$ mirror symmetry, which interchanges $T$ and $U$. Possible applications to flavor physics of the Standard Model require the study of orbifolds of $mathrm{Sp}(4,mathbb Z)$ to obtain chiral fermions. We identify the 13 possible orbifolds and determine their modular flavor symmetries as subgroups of $mathrm{Sp}(4,mathbb Z)$. Some cases correspond to symmetric orbifolds that extend previously discussed cases of $mathrm{SL}(2,mathbb Z)$. Others are based on asymmetric orbifold twists (including mirror symmetry) that do no longer allow for a simple intuitive geometrical interpretation and require further study. Sometimes they can be mapped back to symmetric orbifolds with quantized Wilson lines. The symmetries of $mathrm{Sp}(4,mathbb Z)$ reveal exciting new aspects of modular symmetries with promising applications to flavor model building.
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