Holographic Baryons: Static Properties and Form Factors from Gauge/String Duality

Abstract

In this paper, we study the properties of baryons by using a holographic dual of QCD on the basis of the D4/D8-brane configuration, where baryons are described by a soliton. We first determine the asymptotic behavior of the soliton solution, which allows us to evaluate well-defined currents associated with the U(N f ) L × U(N f ) R chiral symmetry. Using the currents, we compute the static quantities of baryons such as charge radii and magnetic moments, and perform a quantitative comparison with experiments. It is emphasized that not only the nucleon but also excited baryons, such as ∆, N(1440), N(1535), etc., can be analyzed systematically in this model. We also investigate the form factors and find that our form factors agree well with the results that have been well established empirically. Using the form factors, the effective baryon-baryon-meson cubic coupling constants among their infinite towers in the model can be determined. Some physical implications following from these results are discussed. * ) See Ref. 15) for an attempt to include the effect of the ρ meson in the Skyrmion based on the holographic QCD. * ) Our notation is mostly consistent with Ref. 16) except that we do not use the rescaled variables defined in (3.9) of Ref. 16). * ) Again, the same expressions (3 . 32) and (3 . 35) can be found in Ref. 19) but with a different current. Eq. (3 . 32) also agrees with ∆µ an in Ref. 17), if we use the classical value (2 . 15) for ρ 2 . * ) Since the leading contribution to the baryon mass m B is M 0 = 8π 2 κ, we consider m B to be of order λN c . However, we will not use the relation m B ≃ M 0 , since we know that the subleading contributions in m B are not small as discussed in Ref. 16).

N-body nuclear forces at short distances in holographic QCD

“…This is quite analogous to that in pion effective theory; baryons are identified with Skyrmions [10]. Quantization of a single soliton in the SS model [11,12] gives baryon spectra, and also chiral properties such as charge radii and magnetic moments [13] (for other approaches to baryons, see [14]). Mesonbaryon-baryon couplings [13] give a basis of a 2-body nuclear force at long distances, à la the one-mesonexchange picture.…”

“…Quantization of a single soliton in the SS model [11,12] gives baryon spectra, and also chiral properties such as charge radii and magnetic moments [13] (for other approaches to baryons, see [14]). Mesonbaryon-baryon couplings [13] give a basis of a 2-body nuclear force at long distances, à la the one-mesonexchange picture. Short-distance nucleon-nucleon forces were computed [15], which generates a repulsive core with analytic formula for potentials in the large-N c limit.…”

The Witten-Sakai-Sugimoto model: A brief review and some recent results

“…A full-fledged treatment of baryons in the Sakai-Sugimoto model has proved to be very interesting but difficult [42][43][44][45], suggesting that string corrections should be taken into account. Considering the baryon mass, it should be given to leading order by the mass of a D4-brane at the tip of the D8 brane configuration, which is [6] …”

Model-independent form factor relations at largeNc

“…Recently, there has been a wide interest in using gauge/gravity duality in the construction of holographic baryon models [16][17][18][19][20][21][22][23]. These models also implicitly contain large N c limit in the very core of their construction.…”

“…While a "bottom up" phenomenological model [16][17][18] could be shown to satisfy the new model-independent relation, indicating that it had correctly captured the large N c and chiral behavior, the treatment of solitons as instantons [19][20][21][22][23] in the "top down" model of Sakai and Sugimoto [19] failed to satisfy the relation indicating that something was seriously wrong with the approach despite the claimed phenomenological successes of the approach. It was recently shown by Cherman and Ishii [25] that the underlying reason for this appears to be due to a failure of the flat-space instanton approximation.…”