Holographic Models for QCD in the Veneziano Limit (1112.1261v2)

Abstract: We construct a class of bottom-up holographic models with physics comparable to the one expected from QCD in the Veneziano limit of large N_f and N_c with fixed x = N_f/N_c. The models capture the holographic dynamics of the dilaton (dual to the YM coupling) and a tachyon (dual to the chiral condensate), and are parametrized by the real parameter x, which can take values within the range 0 <= x < 11/2. We analyze the saddle point solutions, and draw the phase diagram at zero temperature and density. The backreaction of flavor on the glue is fully included. We find the conformal window for x >= x_c, and the QCD-like phase with chiral symmetry breaking at x < x_c, where the critical value x_c lies close to four. We also find Miransky scaling as x -> x_c as well as Efimov-like saddle points. By calculating the holographic beta-functions, we demonstrate the "walking" behavior of the coupling in the region near and below x_c.

• The paper introduces a novel holographic model that retains quark effects using a dynamic tachyon-dilaton coupling.
• It formulates a phase diagram that distinguishes conformal behavior and chiral symmetry breaking according to varying flavor-to-color ratios.
• It computes holographic beta functions and anomalous dimensions, offering detailed insights into non-perturbative QCD dynamics.

Holographic Models for QCD in the Veneziano Limit

The research article "Holographic Models for QCD in the Veneziano Limit" by Matti Järvinen and Elias Kiritsis introduces and analyzes a specific class of holographic models aimed at capturing the dynamics of Quantum Chromodynamics (QCD) in the Veneziano limit. This limit is formally described by both large numbers of colors ($N_c$) and flavors ($N_f$) while maintaining their ratio $x = N_f/N_c$ fixed. This particular approach is significant due to its ability to preserve leading-order effects of quarks, which are otherwise negligible in the conventional 't Hooft large-$N_c$ limit.

Key Contributions:

1. Veneziano Limit and its Implications: The manuscript begins by setting the theoretical stage for the Veneziano limit, contrasting it with the quenched approximation traditionally studied in large-$N_c$ approaches. It underscores the importance of quark effects in preserving features such as the conformal window and chiral symmetry breaking—phenomena crucial to understanding non-perturbative QCD dynamics.
2. Model Formulation: The paper presents a bottom-up holographic setup combining elements from earlier established holographic approaches for pure Yang-Mills theories with a novel treatment of flavors through a dynamical tachyon field. This tachyon couples to a dilaton field (related to the running coupling of QCD) and a background metric field.
3. Phase Diagram and Dynamical Features:
   • A significant achievement of their work is the construction of a phase diagram demarcating regions with different QCD-like behaviors, identified distinctly by their $x$ values.
   • The authors identify a conformal window for $x_c \leq x < 11/2$, and a QCD-like phase marked by chiral symmetry breaking for $x < x_c$. Importantly, they find that $x_c$ lies near 4.
   • The model accurately captures "walking" dynamics for $x$ values approaching $x_c$ from below, exemplified by Miransky scaling—a characteristic that makes these models pertinent to studying electroweak symmetry breaking scenarios.
4. Numerical Solutions and Beta Functions: An innovative aspect of the research lies in its computation of holographic $\beta$-functions and the associated anomalous dimensions, affording a detailed non-perturbative insight into the QCD dynamics throughout different energy scales.
5. Future Pathways:
   • The paper envisions several applications and improvements to the model. Of particular interest is its potential use in examining meson and glueball spectra, heavy quark energy loss in quark-gluon plasma, and color superconductivity phases at finite density.
   • These models may also serve as a conceptual analogy to paper high-$T_c$ superconductors by considering $x$ as an analogue to doping levels.

Implications for QCD and Beyond

The work elucidates the potentiality of holographic models in capturing complex non-perturbative phenomena in QCD. It also bridges connections to beyond-standard-model physics like walking technicolor models due to the effective description of near-conformal dynamics. By adhering to constraints set by QCD's perturbative structure at ultraviolet scales and matching lattice simulations at lower scales, the paper attempts to present a quantitatively accurate picture that aligns both theoretical and computational milestones.

In summary, "Holographic Models for QCD in the Veneziano Limit" provides a robust theoretical framework with compelling implications not confined to QCD alone but extending to the broader landscape of particle physics. Its detailed exploration of the parameter space and corresponding physical phenomena underscore its utility as a powerful tool in theoretical physics.