F-theory is one of the frameworks where all the Yukawa couplings of grand unified theories are generated and their computation is possible. The Yukawa couplings of charged matter multiplets are supposed to be generated around codimension-3 singularity points of a base complex 3-fold, and that has been confirmed for the simplest type of codimension-3 singularities in recent studies. However, the geometry of F-theory compactifications is much more complicated. For a generic F-theory compactification, such issues as flux configuration around the codimension-3 singularities, field-theory formulation of the local geometry and behavior of zero-mode wavefunctions have virtually never been addressed before. We address all these issues in this article, and further discuss nature of Yukawa couplings generated at such singularities. In order to calculate the Yukawa couplings of low-energy effective theory, however, the local descriptions of wavefunctions on complex surfaces and a global characterization of zero-modes over a complex curve have to be combined together. We found the relation between them by re-examining how chiral charged matters are characterized in F-theory compactification. An intrinsic definition of spectral surfaces in F-theory turns out to be the key concept. As a biproduct, we found a new way to understand the Heterotic-F theory duality, which improves the precision of existing duality map associated with codimension-3 singularities.

We construct a classical solution of vacuum string field theory (VSFT) and study whether it represents the perturbative open string vacuum. Our solution is given as a squeezed state in the Siegel gauge, and it fixes the arbitrary coefficients in the BRST operator in VSFT. We identify the tachyon and massless vector states as fluctuation modes around the classical solution. The tachyon mass squared α ′ m 2 * hata@gauge.scphys.kyoto-u.ac.jp † kawano@hep-th.phys.s.u-tokyo.ac.jp * The descent relation has been studied in VSFT to give expected result under the assumption that the ghost parts of the classical solutions for Dp-branes with different p are common [10,11].

F-theory is one of frameworks in string theory where supersymmetric grand unification is accommodated, and all the Yukawa couplings and Majorana masses of righthanded neutrinos are generated. Yukawa couplings of charged fermions are generated at codimension-3 singularities, and a contribution from a given singularity point is known to be approximately rank 1. Thus, the approximate rank of Yukawa matrices in lowenergy effective theory of generic F-theory compactifications are minimum of either the number of generations N gen = 3 or the number of singularity points of certain types. If there is a geometry with only one E 6 type point and one D 6 type point over the entire 7-brane for SU(5) gauge fields, F-theory compactified on such a geometry would reproduce approximately rank-1 Yukawa matrices in the real world. We found, however, that there is no such geometry. Thus, it is a problem how to generate hierarchical Yukawa eigenvalues in F-theory compactifications. A solution in the literature so far is to take an appropriate factorization limit. In this article, we propose an alternative solution to the hierarchical structure problem (which requires to tune some parameters) by studying how zero mode wavefunctions depend on complex structure moduli. In this solution, the N gen × N gen CKM matrix is predicted to have only N gen entries of order unity without an extra tuning of parameters, and the lepton flavor anarchy is predicted for the lepton mixing matrix. The hierarchy among the Yukawa eigenvalues of the down-type and charged lepton sector is predicted to be smaller than that of the up-type sector, and the Majorana masses of left-handed neutrinos generated through the see-saw mechanism have small hierarchy. All of these predictions agree with what we observe in the real world. We also obtained a precise description of zero mode wavefunctions near the E 6 type singularity points, where the up-type Yukawa couplings are generated.

Cytidine monophospho-N-acetylneuraminic acid (CMP-NeuAc) hydroxylase, which is the key enzyme for the synthesis of N-glycolylneuraminic acid (NeuGc), has been purified from the cytosolic fraction of mouse liver, as described in our previous paper. The amino acid sequences of the purified CMP-NeuAc hydroxylase, and peptides obtained by lysylendopeptidase digestion, were used to synthesize specific oligonucleotide primers. A mouse cDNA clone of the enzyme was obtained by a combination of the polymerase chain reaction and rapid amplification of cDNA ends. The sequence of the clone contained an open reading frame coding for a protein of 577 amino acids with a predicted molecular mass of 66 kDa. The deduced sequence included the amino acid sequences obtained for the purified enzyme and peptides, and a complete match was obtained for 159 residues. The enzyme has neither a signal peptide sequence nor a membrane spanning domain, which is consistent with localization of the enzyme in the cytosol. Transfection of a cDNA construct to COS-1 cells increased the enzyme activity and the amount of NeuGc. Comparison of the sequence with GenBank data indicated that no similar sequence has been reported so far. Northern blot analysis of various mouse tissues with the enzyme cDNA as a probe indicated that expression of NeuGc is related to the level of CMP-NeuAc hydroxylase mRNA. On Southern blot analysis with the same probe, cross-hybridizing bands were detected in the human and fish genomes.

We study the AGT-like conjectured relation of a four-dimensional gauge theory on S 3 × S 1 to two-dimensional q-deformed Yang-Mills theory on a Riemann surface Σ by using a fivedimensional N = 2 supersymmetric Yang-Mills theory on S 3 × Σ, following the conjectured relation of the six-dimensional N = (2, 0) theory on S 1 to the five-dimensional Yang-Mills theory. Our results are in perfect agreement with both of the conjectures.