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.
Highlights
JHEP02(2014)044 on the compact directions is questionable
We investigate properties of baryons in a family of holographic field theories related to the Sakai-Sugimoto model of holographic QCD
The solutions that we find take the form of “oblate instantons”: compared with the SO(4) symmetric configurations, the correct solutions are deformed to configurations with SO(3) symmetry that are spread out more in the field theory directions than in the radial direction
Summary
We give a brief review of the Sakai-Sugimoto model and set up the construction of a baryon in this model. The embedding is described by a curve x4(u) in the cigar geometry, with boundary conditions fixing the position of the probe branes as u → ∞. The gravitational potential of the curved background will work to localize the soliton near the tip of the cigar, at z = 0 This will be counterbalanced by the repulsive potential due to the coupling between the U(1) part of the gauge field and the instanton charge in the Chern-Simons term. Due to the curved background, the actual solution will only be invariant under SO(3) rotations in the field theory directions. Γ is the only parameter in the system It controls the relative strength of the Chern-Simons term; a larger γ will increase the size of the soliton.
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