Nonperturbative QCD Coupling and its $β$ function from Light-Front Holography

Abstract: The light-front holographic mapping of classical gravity in AdS space, modified by a positive-sign dilaton background, leads to a nonperturbative effective coupling $\alpha_s^{AdS}(Q^2)$. It agrees with hadron physics data extracted from different observables, such as the effective charge defined by the Bjorken sum rule, as well as with the predictions of models with built-in confinement and lattice simulations. It also displays a transition from perturbative to nonperturbative conformal regimes at a momentum scale $ \sim 1$ GeV. The resulting $\beta$ function appears to capture the essential characteristics of the full $\beta$ function of QCD, thus giving further support to the application of the gauge/gravity duality to the confining dynamics of strongly coupled QCD. Commensurate scale relations relate observables to each other without scheme or scale ambiguity. In this paper we extrapolate these relations to the nonperturbative domain, thus extending the range of predictions based on $\alpha_s^{AdS}(Q^2)$.

Nonperturbative QCD Coupling from Light-Front Holography

The paper "Nonperturbative QCD Coupling and its $\beta$ Function from Light-Front Holography" proposes a novel approach to understanding the strong coupling dynamics of Quantum Chromodynamics (QCD) using a combination of light-front quantization and the AdS/CFT correspondence. The authors aim to extend the concept of running coupling into the nonperturbative domain, which is typically challenging due to the complexities introduced by gluonic self-coupling and color confinement.

The study employs light-front holography, which maps classical gravity dynamics in anti-de Sitter (AdS) space to the light-front partonic wave functions inherent in QCD. Coupled with a dilaton-modified background to simulate confinement, this framework produces a nonperturbative effective coupling $\alpha_s^{AdS}(Q^2)$ that is consistent with experimental data, models incorporating confinement, and lattice simulations.

Numerical Results and Key Claims

• The paper identifies a transition from perturbative to nonperturbative regimes at a momentum scale approximately 1 GeV by analyzing the resulting $\beta$ function derived from their proposed nonperturbative coupling model.
• The proposed coupling displays an IR fixed point and agrees closely with effective charges derived from the Bjorken sum rule and other lattice QCD predictions.
• The integration of the light-front wavefunctions with the gauge/gravity duality concepts provides compelling analytical results that shed light on infrared QCD dynamics without involving complex numerical computations common in lattice simulations.

Implications and Future Directions

This work supports the gauge/gravity duality application in modeling strongly coupled QCD dynamics. The authors argue that the smooth transition of the nonperturbative coupling to large-momentum transfers provides a coherent picture that merges the traditionally separated perturbative and nonperturbative QCD regimes.

Theoretically, the findings encourage further exploration of gravitational dual descriptions in providing solutions to longstanding challenges in QCD, particularly confinement and the dynamics of bound states. Practically, improved nonperturbative coupling models could enhance the accuracy of QCD predictions at lower energy scales, such as those relevant for the physics of hadrons.

Concluding Remarks

The study highlights the utility of light-front holography in extending perturbative frameworks to embrace nonperturbative QCD effects. The nonperturbative running coupling presented underscores the potential of combined light-front dynamics and holographic techniques in advancing our understanding of strong coupling phenomena in particle physics. As such, the paper offers insightful propositions for overcoming the limitations of traditional perturbative approaches in capturing the full QCD behavior across its various energy regimes.