Teruhiko Kawano

Codimension-3 singularities and Yukawa couplings in F-theory

Abstract 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.

Flavor Structure in F-theory Compactifications

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 low-energy effective theory of generic F-theory compactifications are minimum of either the number of generations Ngen = 3 or the number of singularity points of certain types. If there is a geometry with only one E6 type point and one D6 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 Ngen × Ngen CKM matrix is predicted to have only Ngen 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 E6 type singularity points, where the up-type Yukawa couplings are generated.

More on Dimension-4 Proton Decay Problem in F-theory -- Spectral Surface, Discriminant Locus and Monodromy

Abstract Factorized spectral surface scenario has been considered as one of solutions to the dimension-4 proton decay problem in supersymmetric compactifications of F-theory. It has been formulated in language of gauge theory on 7 + 1 dimensions, but the gauge theory descriptions can capture physics of geometry of F-theory compactification only approximately at best. Given the severe constraint on the renormalizable couplings that lead to proton decay, it is worth studying without an approximation whether or not the proton decay operators are removed completely in this scenario. We clarify how the behavior of spectral surface and discriminant locus are related, study monodromy of 2-cycles in a Calabi–Yau 4-fold geometry, and find that the proton decay operators are likely to be generated in a simple factorization limit of the spectral surface. A list of loopholes in this study, and hence a list of chances to save the factorized spectral surface scenario, is also presented.

MATRIX THEORY ON NONCOMMUTATIVE TORUS

Abstract We consider the compactification of Matrix theory on tori with background antisymmetric tensor field. Douglas and Hull have recently discussed how noncommutative geometry appears on the tori. In this paper, we demonstrate the concrete construction of this compactification of Matrix theory in a similar way to that previously given by Taylor.

Open string fields as matrices

We present a new representation of the string vertices of the cubic open string field theory. By using this three-string vertex, we attempt to identify open string fields as huge-sized matrices by following Wittens idea. By using these huge matrices, we obtain some results about the construction of partial isometries in the algebra of open string fields.

Gauge Invariant Overlaps for Classical Solutions in Open String Field Theory

Abstract We calculate gauge invariant observables for Schnabls solution with analytic method and with the level truncation approximation. We also compute them for the numerical solution initially obtained by Sen and Zwiebach in the level truncation approximation to compare with the one for Schnabls solution. The results are consistent with the expectation that they may be gauge equivalent. We briefly discuss the gauge invariant observables and the action for a marginal solution with a nonsingular current.

Gauge Mediation in String Theory

We show that a large class of phenomenologically viable models for gauge mediation of supersymmetry breaking based on meta-stable vacua can be realized in local Calabi–Yau compactifications of string theory.

String network and 1/4 BPS states in N=4 SU(N) supersymmetric Yang-Mills theory

Abstract We construct the classical configurations of BPS states with 1/4 unbroken supersymmetries in four-dimensional N =4 SU(N+1) supersymmetric Yang-Mills theory, and discuss that these configurations correspond to string networks connecting (N+1) D3-branes in Type IIB string theory.

Open string field theory on noncommutative space

We study Wittens open string field theory in the presence of a constant B field. We construct the string field theory in the operator formalism and find that, compared to the ordinary theory with no B field, the vertices in the resulting theory has an additional factor. The factor makes the zero modes of strings noncommutative. This is in agreement with the results in the first-quantized formulation. We also discuss background independence of the purely cubic action derived from the above string field theory and then find a redefinition of string fields to remove the additional factor from the vertex. Furthermore, we briefly discuss the supersymmetric extension of our string field theory.

S-duality from OM-theory

Abstract We study the compactification of OM-theory on tori and show a simple heuristic derivation of the S -duals of noncommutative open string theory in diverse dimensions from the OM-theoretical point of view. In particular, we identify the S -duality between noncommutative open string theory and noncommutative Yang–Mills theory in 3+1 dimensions as the exchange of two circles of a torus on which OM-theory is compactified. Also, we briefly discuss T -duality between noncommutative open string theories.