Solution of the boundary problem for the axial-vector field in the hard-wall AdS/QCD model

TL;DR

This paper presents an analytical and numerical solution to the axial-vector boundary problem in the hard-wall AdS/QCD model, advancing the understanding of holographic QCD models.

Contribution

It introduces a new scheme for solving the boundary value problem, utilizing necessary conditions to establish Fredholm solvability in the hard-wall AdS/QCD framework.

Findings

Derived fundamental solutions for the axial-vector field equation.

Established main relations and necessary conditions for solutions.

Applied an iterative method to solve the integral equation with Volterra and Fredholm terms.

Abstract

We solve an equation of motion for the axial-vector field under boundary conditions of the bulk-to-boundary propagator in the framework of the hard-wall model of AdS/QCD. The equation is reduced to the form of a homogeneous ordinary differential equation with varying coefficients. We solve conjugate equations and find fundamental solutions. This allows us to establish main relations and necessity conditions. The integral equation has both Volterra and Fredholm terms and was solved by the iteration method. We apply a new scheme to solve the equation, since all linearly independent necessary conditions for the existence of a solution were defined and used to establish a sufficient condition for Fredholm solvability of the problem.