Numerical analysis of a baryon and its dilatation modes in holographic QCD

TL;DR

This paper models baryons in holographic QCD as vortex solutions in a reduced Abelian Higgs theory, numerically analyzing their size oscillations and identifying the Roper resonance as a dilatation mode.

Contribution

It introduces a novel vortex-based description of baryons in holographic QCD and numerically computes their dilatation modes, linking them to observed nucleon excitations.

Findings

Baryons are described as Abrikosov vortices in a reduced 2D theory.

The lowest dilatation mode energy is 577 MeV.

The Roper resonance N*(1440) is identified as a baryon dilatation mode.

Abstract

We investigate a baryon and its dilatation modes in holographic QCD based on the Sakai-Sugimoto model, which is expressed as a 1+4 dimensional U($N_f$) gauge theory in the flavor space. For spatially rotational symmetric systems, we apply a generalized version of the Witten Ansatz, and reduce 1+4 dimensional holographic QCD into a 1+2 dimensional Abelian Higgs theory in a curved space. In the reduced theory, the holographic baryon is described as a two-dimensional topological object of an Abrikosov vortex. We numerically calculate the baryon solution of holographic QCD using a fine and large lattice with spacing of 0.04 fm and size of 10 fm. Using the relation between the baryon size and the zero-point location of the Higgs field in the description with the Witten Ansatz, we investigate a various-size baryon through this vortex description. As time-dependent size-oscillation modes (dilatation modes) of a baryon, we numerically obtain the lowest excitation energy of 577 MeV and deduce the dilatational excitation of a nucleon to be the Roper resonance N$^*$(1440).