Holographic Baryons from Oblate Instantons

Abstract

We investigate properties of baryons in a family of holographic field theories related to the Sakai-Sugimoto model of holographic QCD. Starting with the $N_f=2$ Sakai-Sugimoto model, we truncate to a 5D Yang-Mills action for the gauge fields associated with the noncompact directions of the flavour D8-branes. We define a free parameter $\gamma$ that controls the strength of this Yang-Mills term relative to the Chern-Simons term that couples the abelian gauge field to the SU(2) instanton density. Moving away from $\gamma = 0$ should incorporate some of the effects of taking the Sakai-Sugimoto model away from large 't Hooft coupling $\lambda$. In this case, the baryon ground state corresponds to an oblate SU(2) instanton on the bulk flavour branes: the usual SO(4) symmetric instanton is deformed to spread more along the field theory directions than the radial direction. We numerically construct these anisotropic instanton solutions for various values of $\gamma$ and calculate the mass and baryon charge profile of the corresponding baryons. Using the value $\gamma = 2.55$ that has been found to best fit the mesonic spectrum of QCD, we find a value for the baryon mass of 1.19 GeV, significantly more realistic than the value 1.60 GeV computed previously using an SO(4) symmetric ansatz for the instanton.