TY - JOUR

T1 - Confinement Potential in a Soft-Wall Holographic Model with a Hydrogen-like Spectrum

AU - Afonin, Sergey

AU - Solomko, Timofey

N1 - Afonin, S.; Solomko, T. Confinement Potential in a Soft-Wall Holographic Model with a Hydrogen-like Spectrum. Universe 2023, 9, 114. https://doi.org/10.3390/universe9030114

PY - 2023/2/22

Y1 - 2023/2/22

N2 - It is well known that the soft-wall holographic model for QCD successfully reproduces not only the linear Regge spectrum, but also, via the holographic Wilson confinement criterion, the "linear plus Coulomb" confinement potential, which is similar to the Cornell potential. This property could be interpreted as a holographic counterpart of the hadron string picture, where the linearly rising potential and Regge-like spectrum are directly related. However, such a relation does not exist in the bottom-up holographic approach. Namely, the Cornell-like potentials arise in a broad class of bottom-up holographic models. The standard soft-wall model is merely a particular representative of this class. This fact is relatively unknown, so we provide a comprehensive discussion of the point. As an example, we consider a soft-wall-like model with linear dilaton background in the metric. This model leads to a hydrogen-like spectrum. A "linear plus Coulomb" confinement potential within this model is calculated. The calculation of renormalized potential at short distances turns out to be complicated by a new subtlety that was skipped in general discussions of the issue existing in the literature. However, the confinement potential of the model is shown to be not very different from the potential obtained in the standard soft-wall model with a quadratic background.

AB - It is well known that the soft-wall holographic model for QCD successfully reproduces not only the linear Regge spectrum, but also, via the holographic Wilson confinement criterion, the "linear plus Coulomb" confinement potential, which is similar to the Cornell potential. This property could be interpreted as a holographic counterpart of the hadron string picture, where the linearly rising potential and Regge-like spectrum are directly related. However, such a relation does not exist in the bottom-up holographic approach. Namely, the Cornell-like potentials arise in a broad class of bottom-up holographic models. The standard soft-wall model is merely a particular representative of this class. This fact is relatively unknown, so we provide a comprehensive discussion of the point. As an example, we consider a soft-wall-like model with linear dilaton background in the metric. This model leads to a hydrogen-like spectrum. A "linear plus Coulomb" confinement potential within this model is calculated. The calculation of renormalized potential at short distances turns out to be complicated by a new subtlety that was skipped in general discussions of the issue existing in the literature. However, the confinement potential of the model is shown to be not very different from the potential obtained in the standard soft-wall model with a quadratic background.

KW - AdS/QCD

KW - heavy-quark potential

UR - https://www.mdpi.com/2218-1997/9/3/114

M3 - Article

VL - 9

JO - Universe

JF - Universe

SN - 2218-1997

IS - 3

M1 - 114

ER -