Effective action in spherical domains

The effective action on an orbifolded sphere is computed for minimally coupled scalar fields. The results are presented in terms of derivatives of Barnes zeta-functions and it is shown how these may be evaluated. Numerical values are shown. An analytical, heat-kernel derivation of the Ces\`aro-Fedorov formula for the number of symmetry planes of a regular solid is also presented.Comment: 18 pages, Plain TeX (Mailer oddities possibly corrected.

Gauge coupling flux thresholds, exotic matter and the unification scale in F-SU(5) GUT

We explore the gauge coupling relations and the unification scale in F-theory SU(5) GUT broken down to the Standard Model by an internal U(1)Y gauge flux. We consider variants with exotic matter representations which may appear in these constructions and investigate their role in the effective field theory model. We make a detailed investigation on the conditions imposed on the extraneous matter to raise the unification scale and make the color triplets heavy in order to avoid fast proton decay. We also discuss in brief the implications on the gaugino masses.Comment: 20 pages, 3 figures, references and extended comments on KK thresholds effects adde

Quark mass dependence of the nucleon axial-vector coupling constant

We study the quark mass expansion of the axial-vector coupling constant g_A of the nucleon. The aim is to explore the feasibility of chiral effective field theory methods for extrapolation of lattice QCD results - so far determined at relatively large quark masses corresponding to pion masses larger than 0.6 GeV - down to the physical value of the pion mass. We compare two versions of non-relativistic chiral effective field theory: One scheme restricted to pion and nucleon degrees of freedom only, and an alternative approach which incorporates explicit Delta(1230) resonance degrees of freedom. It turns out that, in order to approach the physical value of g_A in a leading-one-loop calculation, the inclusion of the explicit Delta(1230) degrees of freedom is crucial. With information on important higher order couplings constrained from analyses of inelastic pion production processes, a chiral extrapolation function for g_A is obtained, which works well from the chiral limit across the physical point into the region of present lattice data. The resulting enhancement of our extrapolation function near the physical pion mass is found to arise from an interplay between long- and short- distance physics.Comment: 21 pages, LaTeX, 7 figure

Energy States of Colored Particle in a Chromomagnetic Field

The unitary transformation, which diagonalizes squared Dirac equation in a constant chromomagnetic field is found. Applying this transformation, we find the eigenfunctions of diagonalized Hamiltonian, that describe the states with definite value of energy and call them energy states. It is pointed out that, the energy states are determined by the color interaction term of the particle with the background chromofield and this term is responsible for the splitting of the energy spectrum. We construct supercharge operators for the diagonal Hamiltonian, that ensure the superpartner property of the energy states.Comment: 25 pages, some calculation details have been removed, typos correcte

Zeta function determinant of the Laplace operator on the DD-dimensional ball

We present a direct approach for the calculation of functional determinants of the Laplace operator on balls. Dirichlet and Robin boundary conditions are considered. Using this approach, formulas for any value of the dimension, $D$, of the ball, can be obtained quite easily. Explicit results are presented here for dimensions $D=2,3,4,5$ and $6$.Comment: 22 pages, one figure appended as uuencoded postscript fil

Sum rules and dualities for generalized parton distributions: is there a holographic principle?

To leading order approximation, the physical content of generalized parton distributions (GPDs) that is accessible in deep virtual electroproduction of photons or mesons is contained in their value on the cross-over trajectory. This trajectory separates the t-channel and s-channel dominated GPD regions. The underlying Lorentz covariance implies correspondence between these two regions through their relation to GPDs on the cross-over trajectory. This point of view leads to a family of GPD sum rules which are a quark analogue of finite energy sum rules and it guides us to a new phenomenological GPD concept. As an example, we discuss the constraints from the JLab/Hall A data on the dominant u-quark GPD H. The question arises whether GPDs are governed by some kind of holographic principle.Comment: 45 pages, 4 figures, Sect. 2 reorganized for clarity. Typos in Eq. (20) corrected. 4 new refs. Matches published versio

Moments of isovector quark distributions from lattice QCD

We present a complete analysis of the chiral extrapolation of lattice moments of all twist-2 isovector quark distributions, including corrections from Nπ and Δπ loops. Even though the Δ resonance formally gives rise to higher order non-analytic structure, the coefficients of the higher order terms for the helicity and transversity moments are large and cancel much of the curvature generated by the wave function renormalization. The net effect is that, whereas the unpolarized moments exhibit considerable curvature, the polarized moments show little deviation from linearity as the chiral limit is approached