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.Comment: 51 page

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

Pure Natural Inflation

We point out that a simple inflationary model in which the axionic inflaton couples to a pure Yang-Mills theory may give the scalar spectral index (n_s) and tensor-to-scalar ratio (r) in complete agreement with the current observational data.Comment: 4 pages, 3 figures, published versio

Mass Generation for an Ultralight Axion

If a global chiral symmetry is explicitly broken by anomalies in nonabelian gauge theories, a pseudo Nambu-Goldstone boson (axion) associated with a spontaneous breakdown of such a global symmetry acquires a mass through nonperturbative instanton effects. We calculate the axion mass assuming a supersymmetric SU(2) gauge theory and show that the axion obtains an extremely small mass when the SU(2) gauge symmetry is broken down at very high energy, say at the Planck scale. We identify the axion with a hypothetical ultralight boson field proposed to account for a small but nonzero cosmological constant suggested from recent cosmological observations.Comment: 11 pages, Late