Constraining the Kahler Moduli in the Heterotic Standard Model

Phenomenological implications of the volume of the Calabi-Yau threefolds on the hidden and observable M-theory boundaries, together with slope stability of their corresponding vector bundles, constrain the set of Kaehler moduli which give rise to realistic compactifications of the strongly coupled heterotic string. When vector bundles are constructed using extensions, we provide simple rules to determine lower and upper bounds to the region of the Kaehler moduli space where such compactifications can exist. We show how small these regions can be, working out in full detail the case of the recently proposed Heterotic Standard Model. More explicitely, we exhibit Kaehler classes in these regions for which the visible vector bundle is stable. On the other hand, there is no polarization for which the hidden bundle is stable.Comment: 28 pages, harvmac. Exposition improved, references and one figure added, minor correction

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2006 年4 月～2010 年3 月の神経線維腫症1 型に伴う脊柱変形手術例10 例中3 例に肋骨頭の脊柱管内脱臼がみられた.症例1 は6 歳の男児でT4-8:74°,T8-11:72° の側弯があり,左第4 と第5 肋骨頭の脊柱管内への陥入を認めた.症例2 は11 歳の男児でT3-7:100° の側弯とT3-T9:90° の後弯があり,左第6 肋骨頭が脊柱管内へ脱臼し,脊髄を圧排していた.症例3 は27 歳の女性でT6～9:73°,T9～12:68° の側弯とT6-10:91°の後弯を認め,右第7 肋骨頭の脊柱管内脱臼がみられた.本病態の報告例は少ないが,決して希な病態ではなくdystrophic change を伴う脊柱変形においては,肋骨頭の脊柱管内脱臼による潜在的リスクに注意する必要があると考える.Spinal deformities are common features in neurofibromatosistype-1( NF-1). Several types of deformities have been reported, however, intraspinal rib head dislocation (IRD)due to dystrophic change is very rare and not well understood. Between April 2006 and March 2010, we experienced3 patients with IRD out of 10 consecutive patients who underwent surgical treatment for dystrophic spinal deformities in NF-1. Case 1:A 6-year-old boy who had 74 ° short angular scoliosis at T4-8 and 72 ° at T8-11 underwent surgery in our institute. CT myelography demonstrated dystrophic changes with for aminal enlargement, vertebral body scalloping, rib penciling and mild IRD. He underwent the Growing Rod techniques and finally underwent posterior spinal fusion (PSF) from T1 to L2 combined with prophylactic rib head resection followed by anterior spinal fusion(ASF) with autologous fibular strut graft. No neurological complications were observed postoperatively and complete bony fusions were achieved. Case 2:Neurologically intact11-year-old boy presented with spinal deformity and caféau-lait spots. Radiography showed 100 ° scoliosis at T3-7and 72 ° at T3-9. CT myelography demonstrated dystrophic changes and IRD and impingement of spinal cord. He underwent PSF with removal of the T6 rib head followed by ASF. Case 3:A 27-year-old woman presented with back pain and spinal deformities. Radiography showed 73 °scoliosis at T6-9 and 91 ° at T9-12. CT myelography demonstrated dystrophic changes and IRD. She also underwentPSF with removal of T7 rib head followed by ASF. AllIRDs were observed at the apex of the convex side of scoliosis.It has a potential risk of spinal cord compression and may cause paraplegia or paraparesis. Therefore, high degree of suspicion is warranted for the treatments of scoliosis with intraspinal rib displacement in NF-1