arXiv subjects

Taizan Watari

Publications and source records attributed to Taizan Watari.

At least 37 records · Page 2Linked to original sources

arXiv2015

Statistics of Flux Vacua for Particle Physics

Supersymmetric flux compactification of F-theory in the geometric phase yields numerous vacua, and provides an ensemble of low-energy effective theories with different symmetry, matter multiplicity and Lagrangian parameters. Theoretical tools have already been developed so that we can study how the statistics of flux vacua depend on the choice of symmetry and some of Lagrangian parameters. In this article, we estimate the fraction of i) vacua that have a U(1) symmetry for spontaneous R-parity violation, and ii) those that realise ideas which achieve hierarchical eigenvalues of the Yukawa matrices. We also learn a lesson that the number of flux vacua is reduced very much when the unbroken $U(1)_Y$ symmetry is obtained from a non-trivial Mordell--Weil group, while it is not when $U(1)_Y$ is in SU(5) unification. It also turns out that vacua with an approximate U(1) symmetry forms a locus of accumulation points of the flux vacua distribution.

hep-th↗

arXiv2014

The Vertical, the Horizontal and the Rest: anatomy of the middle cohomology of Calabi-Yau fourfolds and F-theory applications

The four-form field strength in F-theory compactifications on Calabi-Yau fourfolds takes its value in the middle cohomology group $H^4$. The middle cohomology is decomposed into a vertical, a horizontal and a remaining component, all three of which are present in general. We argue that a flux along the remaining or vertical component may break some symmetry, while a purely horizontal flux does not influence the unbroken part of the gauge group or the net chirality of charged matter fields. This makes the decomposition crucial to the counting of flux vacua in the context of F-theory GUTs. We use mirror symmetry to derive a combinatorial formula for the dimensions of these components applicable to any toric Calabi--Yau hypersurface, and also make a partial attempt at providing a geometric characterization of the four-cycles Poincaré dual to the remaining component of $H^4$. It is also found in general elliptic Calabi-Yau fourfolds supporting SU(5) gauge symmetry that a remaining component can be present, for example, in a form crucial to the symmetry breaking ${\rm SU}(5) \longrightarrow {\rm SU}(3)_C \times {\rm SU}(2)_L \times {\rm U}(1)_Y$. The dimension of the horizontal component is used to derive an estimate of the statistical distribution of the number of generations and the rank of 7-brane gauge groups in the landscape of F-theory flux vacua.

hep-th↗

arXiv2014

Distribution of the Number of Generations in Flux Compactifications

Flux compactification of string theory generates an ensemble with a large number of vacua called the landscape. By using the statistics of various properties of low-energy effective theories in the string landscape, one can therefore hope to provide a scientific foundation to the notion of naturalness. This article discusses how to answer such questions of practical interest by using flux compactification of F-theory. It is found that the distribution is approximately in a factorized form given by the distribution of the choice of 7-brane gauge group, that of the number of generations $N_{\rm gen}$ and that of effective coupling constants. The distribution of $N_{\rm gen}$ is approximately Gaussian for the range $|N_{\rm gen}| \lesssim 10$. The statistical cost of higher-rank gauge groups is also discussed.

hep-ph↗

arXiv2014

Issues in Complex Structure Moduli Inflation

Supersymmetric compactification with moderately large radius (${\rm Re}< T > \sim {\cal O}(10)$ or more) not only accommodates supersymmetric unification, but also provides candidates for an inflaton in the form of geometric moduli; the value of ${\rm Re}< T > > 1$ may be used as a parameter that brings corrections to the inflaton potential under control. Motivated by a bottom-up idea "right-handed sneutrino inflation" scenario, we study whether complex structure moduli can play some role during the slow-roll inflation and/or reheating process in this moderately large radius regime. Even when we allow a tuning introduced by Kallosh and Linde, the barrier of volume stabilization potential from gaugino condensation racetrack superpotential can hardly be as high as $(10^{16} \; {\rm GeV})^4$ for generic choice of parameters in this regime. It is also found that even very small deformation of complex structure during inflation/reheating distorts the volume stabilization potential, so that the volume stabilization imposes tight constraints on large-field inflation scenario involving evolution of complex structure moduli. A few ideas of satisfying those constraints in string theory are also discussed.

hep-th↗

arXiv2014

Skewness Dependence of GPD / DVCS, Conformal OPE and AdS/CFT Correspondence II: a holographic model of GPD

Traditional idea of Pomeron/Reggeon description for hadron scattering is now being given theoretical foundation in gravity dual descriptions, where Pomeron corresponds to exchange of spin-$j \in 2\mathbb{Z}$ states in the graviton trajectory. Deeply virtual Compton scattering (DVCS) is essentially a 2 to 2 scattering process of a hadron and a photon, and hence one should be able to study non-perturbative aspects (GPD) of this process by the Pomeron/Reggeon process in gravity dual. We find, however, that even one of the most developed formulations of gravity dual Pomeron (Brower--Polchinski--Strassler--Tan (BPST) 2006) is not able to capture skewness dependence of GPD properly. In Part I (arXiv:1212.3322), therefore, we computed Reggeon wavefunctions on AdS$_5$ so that the formalism of BPST can be generalized. In this article, Part II, we use the wavefunctions to determine the DVCS amplitude, bring it to the form of conformal OPE/collinear factorization, and extract a holographic model of GPD, which naturally fits into the framework known as "dual parametrization" or "(conformal) collinear factorization approach".

hep-ph↗

arXiv2014

The Noether-Lefschetz Problem and Gauge-Group-Resolved Landscapes: F-Theory on K3 x K3 as a Test Case

Four-form flux in F-theory compactifications not only stabilizes moduli, but gives rise to ensembles of string vacua, providing a scientific basis for a stringy notion of naturalness. Of particular interest in this context is the ability to keep track of algebraic information (such as the gauge group) associated with individual vacua while dealing with statistics. In the present work, we aim to clarify conceptual issues and sharpen methods for this purpose, using compactification on ${\rm K3} \times {\rm K3}$ as a test case. Our first approach exploits the connection between the stabilization of complex structure moduli and the Noether-Lefschetz problem. Compactification data for F-theory, however, involve not only a four-fold (with a given complex structure) $Y_4$ and a flux on it, but also an elliptic fibration morphism $Y_4 \longrightarrow B_3$, which makes this problem complicated. The heterotic-F-theory duality indicates that elliptic fibration morphisms should be identified modulo isomorphism. Based on this principle, we explain how to count F-theory vacua on ${\rm K3} \times {\rm K3}$ while keeping the gauge group information. Mathematical results reviewed/developed in our companion paper are exploited heavily. With applications to more general four-folds in mind, we also clarify how to use Ashok-Denef-Douglas' theory of the distribution of flux vacua in order to deal with statistics of sub-ensembles tagged by a given set of algebraic/topological information. As a side remark, we extend the heterotic/F-theory duality dictionary on flux quanta and elaborate on its connection to the semistable degeneration of a K3 surface.

hep-th↗

arXiv2013

On the Classification of Elliptic Fibrations modulo Isomorphism on K3 Surfaces with large Picard Number

Motivated by a problem originating in string theory, we study elliptic fibrations on K3 surfaces with large Picard number modulo isomorphism. We give methods to determine upper bounds for the number of inequivalent K3 surfaces sharing the same frame lattice. For any given Neron--Severi lattice $S_X$, such a bound on the `multiplicity' can be derived by investigating the quotient of the isometry group of $S_X$ by the automorphism group. The resulting bounds are strongest for large Picard numbers and multiplicities of unity do indeed occur for a number of K3 surfaces with Picard number 20. Under a few extra conditions, a more refined analysis is also possible by explicitly studying the embedding of $S_X$ into the even unimodular lattice ${\rm II}_{1,25}$ and exploiting the detailed structure of the isometry groups of $S_X$ and ${\rm II}_{1,25}$. We illustrate these methods in examples and derive bounds for the number of elliptic fibrations on Kummer surfaces of Picard numbers 17 and 20. As an intermediate step, we also discuss coarser classification schemes and review known results.

math.AG↗

arXiv2013

On Singular Fibres in F-Theory

In this paper, we propose a connection between the field theory local model (Katz-Vafa field theory) and the type of singular fibre in flat crepant resolutions of elliptic Calabi-Yau fourfolds, a class of fourfolds considered by Esole and Yau. We review the analysis of degenerate fibres for models with gauge groups SU(5) and SO(10) in detail, and observe that the naively expected fibre type is realized if and only if the Higgs vev in the field theory local model is unramified. To test this idea, we implement a linear (unramified) Higgs vev for the `E6' Yukawa point in a model with gauge group SU(5) and verify that this indeed leads to a fibre of Kodaira type IV*. Based on this observation, we argue i) that the singular fibre types appearing in the fourfolds studied by Esole-Yau are not puzzling at all, (so that this class of fourfolds does not have to be excluded from the candidate of input data of some yet-unknown formulation of F-theory) and ii) that such fourfold geometries also contain more information than just the eigenvalues of the Higgs field vev configuration in the field theory local models.

hep-th↗

arXiv2012

Skewness Dependence of GPD / DVCS, Conformal OPE and AdS/CFT Correspondence I: Wavefunctions of Regge Trajectory

Traditional idea of Pomeron/Reggeon description for hadron scattering is now being given theoretical foundation in gravity dual descriptions, where Pomeron corresponds to exchange of spin-j\in 2Z states in the graviton trajectory. Deeply virtual compton scattering (DVCS) is essentially a 2 to 2 scattering process of a hadron and a photon, and hence one should be able to study non-perturbative aspects (GPD) of this process by the "Pomeron" process in gravity dual. We find, however, that even the most developed formulation of gravity dual Pomeron (Brower--Polchinski--Strassler--Tan (BPST) 2006) is not able to capture skewness dependence of GPD properly. Conformal operator product expansion allows us to determine DVCS amplitude in terms of matrix elements of primary operators, which should then be given by wavefunctions on warped spacetime. We determined all the necessary wavefunctions on AdS$_5$ as an expression holomorphic in $j$, which will then be used (in our forthcoming publication) to determine GPD through inverse Mellin transformation. This approach will extend the formulation of BPST.

hep-th↗

arXiv2012

Naive Dimensional Analysis in Holography

Naive dimensional analysis (NDA) is a widely used ansatz to estimate coupling constants among composite states emerging from dynamics of a strongly coupled gauge theory. However, the validity of NDA is still unclear because of the difficulty in calculating these quantities in strongly coupled theories. We examine the NDA ansatz using gauge/string duality, by estimating glueball coupling constants from gravitational description. The NDA scaling rule for coupling constants of some types of glueballs is verified and extended by both generic estimation and numerical calculations. The scaling rule verified in this article can be applied to some class of quiver gauge theories as well, not just to gauge theories with a single gauge group $SU(N_c)$.

hep-ph↗

arXiv2012

A Note on Kahler Potential of Charged Matter in F-theory

We study the Kahler potential of charged matter fields, whose profiles have a peak on their matter curve --- on an "intersection" of 7-branes, in an F-theory compactification. It is shown that the Kahler potential is exactly given by the integral over the matter curve, but not by the integral over the whole GUT surface of 7-branes.

hep-th↗

arXiv2012

Constraints on GUT 7-brane Topology in F-theory

We study the relation between phenomenological requirements and the topology of the surfaces that GUT 7-branes wrap in F-theory compactifications. In addition to the exotic matter free condition in the hypercharge flux scenario of SU(5)_{GUT} breaking, we analyze a new condition that comes from a discrete symmetry aligning the contributions to low-energy Yukawa matrices from a number of codimension-three singularity points. We see that the exotic matter free condition excludes Hirzebruch surfaces (except ${\mathbb F}_0$) as the GUT surface, correcting an existing proof in the literature. We further find that the discrete symmetry for the alignment of the Yukawa matrices excludes del Pezzo surfaces and a rational elliptic surface as the GUT surface. Therefore, some GUT 7-brane surfaces are good for some phenomenological requirements, but sometimes not for others, and this aspect should be kept in mind in geometry search in F-theory compactifications.

hep-th↗

arXiv2011

Investigating Generalized Parton Distribution in Gravity Dual

Generalized parton distribution (GPD) contains rich information of partons in a hadron, including transverse profile, and is also non-perturbative information necessary in describing a variety of hard processes, such as meson leptoproduction and double deeply virtual Compton scattering (DDVCS). In order to unveil non-perturbative aspects of GPD, we study DDVCS at small $x$ in gravitational dual description. Using the complex spin $j$-plane representation of DDVCS amplitude, we show that GPD is well-defined and can be extracted from the amplitude even in the strong coupling regime. It also turns out that the saddle point value in the $j$-plane representation plays an important role; there are two phases in the imaginary part of the amplitude of DDVCS and GPD, depending on relative position of the saddle point and the leading pole in the $j$-plane, and crossover between them is induced by the change of the kinematical variables. The saddle point value also directly controls kinematical variable dependence of many observables in one of the two phases, and indeed the dependence is qualitatively in nice agreement with HERA measurements. Such observation that the gravity dual shares basic properties of the real world QCD suggests that information from BFKL theory might be used to reduce error in the gravity dual predictions of the form factor and of GPD. This article also serves as a brief summery of a preprint arXiv:1105.2999.

hep-ph↗

arXiv2011

High--Energy Photon--Hadron Scattering in Holographic QCD

This article provides an in-depth look at hadron high energy scattering by using gravity dual descriptions of strongly coupled gauge theories. Just like deeply inelastic scattering (DIS) and deeply virtual Compton scattering (DVCS) serve as clean experimental probes into non-perturbative internal structure of hadrons, elastic scattering amplitude of a hadron and a (virtual) "photon" in gravity dual can be exploited as a theoretical probe. Since the scattering amplitude at sufficiently high energy (small Bjorken x) is dominated by parton contributions (= Pomeron contributions) even in strong coupling regime, there is a chance to learn a lesson for generalized parton distribution (GPD) by using gravity dual models. We begin with refining derivation of Brower-Polchinski-Strassler-Tan (BPST) Pomeron kernel in gravity dual, paying particular attention to the role played by complex spin variable j. The BPST Pomeron on warped spacetime consists of a Kaluza-Klein tower of 4D Pomerons with non-linear trajectories, and we clarify the relation between Pomeron couplings and Pomeron form factor. We emphasize that the saddle point value j^* of the scattering amplitude in the complex j-plane representation is a very important concept in understanding qualitative behavior of the scattering amplitude. The total Pomeron contribution to the scattering is decomposed into the saddle point contribution and at most a finite number of pole contributions, and when the pole contributions are absent (which we call saddle point phase), kinematical variable (q,x,t) dependence of ln (1/q) evolution and ln(1/x) evolution parameters gamma_eff. and lambda_eff. in DIS and t-slope parameter B of DVCS in HERA experiment are all reproduced qualitatively in gravity dual.

hep-ph↗

arXiv2010

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 right-handed 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 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 x 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. 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.

hep-th↗

arXiv2009

New Aspects of Heterotic--F Theory Duality

In order to understand both up-type and down-type Yukawa couplings, F-theory is a better framework than the perturbative Type IIB string theory. The duality between the Heterotic and F-theory is a powerful tool in gaining more insights into F-theory description of low-energy chiral multiplets. Because chiral multiplets from bundles /\^2 V and /\^2 V^x as well as those from a bundle V are all involved in Yukawa couplings in Heterotic compactification, we need to translate descriptions of all those kinds of matter multiplets into F-theory language through the duality. We find that chiral matter multiplets in F-theory are global holomorphic sections of line bundles on what we call covering matter curves. The covering matter curves are formulated in Heterotic theory in association with normalization of spectral surface, while they are where M2-branes wrapped on a vanishing two-cycle propagate in F-theory. Chirality formulae are given purely in terms of (possibly primitive) four-form flux. In order to complete the translation, the dictionary of the Heterotic--F theory duality has to be refined in some aspects. A precise map of spectral surface and complex structure moduli is obtained, and with the map, we find that divisors specifying the line bundles correspond precisely to codimension-3 singularities in F-theory.

hep-th↗

arXiv2009

GUT Relations from String Theory Compactifications

Wilson line on a non-simply connected manifold is a nice way to break SU(5) unified symmetry, and to solve the doublet--triplet splitting problem. This mechanism also requires, however, that the two Higgs doublets are strictly vector-like under all underlying gauge symmetries, and consequently there is a limit in a class of modes and their phenomenology for which the Wilson line can be used. An alternative is to turn on a non-flat line bundle in the U(1)_Y direction on an internal manifold, which does not have to be non-simply connected. The U(1)_Y gauge field has to remain in the massless spectrum, and its coupling has to satisfy the GUT relation. In string theory compactifications, however, it is not that easy to satisfy these conditions in a natural way; we call it U(1)_Y problem. In this article, we explain how the problem is solved in some parts of moduli space of string theory compactifications. Two major ingredients are an extra strongly coupled U(1) gauge field and parametrically large volume for compactification that is also essential in accounting for the hierarchy between the Planck scale and the GUT scale. Heterotic-M theory vacua and F-theory vacua are discussed. This article also shows that the toroidal orbifold GUT approach using discrete Wilson lines corresponds to the non-flat line-bundle breaking above when orbifold singularities are blown up. Thus, the orbifold GUT approach also suffers from the U(1)_Y problem, and this article shows how to fix it.

hep-th↗