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Exploring improved holographic theories for QCD: Part I

U. Gursoy, E. Kiritsis

TL;DR

The paper develops a holographic framework for large-$N_c$ QCD in five dimensions using a gravity-dilaton-axion action, where the dilaton potential $V(\lambda)$ is in one-to-one correspondence with the exact QCD $\beta$-function, determining the full vacuum structure and RG flow. The UV region is asymptotically AdS$_5$ with logarithmic corrections reflecting asymptotic freedom, while IR backgrounds can be confining with good (Gubser) singularities and, in certain cases, yield linear confinement for glueballs and mesons. A first-order formalism via the phase variable $X(\Phi)$ links the geometry to the gauge-theory $\beta$-function, and the analysis accounts for $\alpha'$ corrections, UV universality, and scheme dependence, culminating in explicit background examples including a standard QCD-like two-loop beta-function and an IR-fixed-point scenario. The work presents a predictive, phenomenological holographic model that connects spectral properties (glueballs, mesons) and topological physics (the QCD $\theta$-angle) to the RG structure of QCD, with Part II detailing IR spectra and further phenomenology.

Abstract

Various holographic approaches to QCD in five dimensions are explored using input both from the putative non-critical string theory as well as QCD. It is argued that a gravity theory in five dimensions coupled to a dilaton and an axion may capture the important qualitative features of pure QCD. A part of the higher alpha' corrections are resummed into a dilaton potential. The potential is shown to be in one-to-one correspondence with the exact beta-function of QCD, and its knowledge determines the full structure of the vacuum solution. The geometry near the UV boundary is that of AdS_5 with logarithmic corrections reflecting the asymptotic freedom of QCD. We find that all relevant confining backgrounds have an IR singularity of the "good" kind that allows unambiguous spectrum computations. Near the singularity the 't Hooft coupling is driven to infinity. Asymptotically linear glueball masses can also be achieved. The classification of all confining asymptotics, the associated glueball spectra and meson dynamics are addressed in a companion paper, ArXiv:0707.1349

Exploring improved holographic theories for QCD: Part I

TL;DR

The paper develops a holographic framework for large- QCD in five dimensions using a gravity-dilaton-axion action, where the dilaton potential is in one-to-one correspondence with the exact QCD -function, determining the full vacuum structure and RG flow. The UV region is asymptotically AdS with logarithmic corrections reflecting asymptotic freedom, while IR backgrounds can be confining with good (Gubser) singularities and, in certain cases, yield linear confinement for glueballs and mesons. A first-order formalism via the phase variable links the geometry to the gauge-theory -function, and the analysis accounts for corrections, UV universality, and scheme dependence, culminating in explicit background examples including a standard QCD-like two-loop beta-function and an IR-fixed-point scenario. The work presents a predictive, phenomenological holographic model that connects spectral properties (glueballs, mesons) and topological physics (the QCD -angle) to the RG structure of QCD, with Part II detailing IR spectra and further phenomenology.

Abstract

Various holographic approaches to QCD in five dimensions are explored using input both from the putative non-critical string theory as well as QCD. It is argued that a gravity theory in five dimensions coupled to a dilaton and an axion may capture the important qualitative features of pure QCD. A part of the higher alpha' corrections are resummed into a dilaton potential. The potential is shown to be in one-to-one correspondence with the exact beta-function of QCD, and its knowledge determines the full structure of the vacuum solution. The geometry near the UV boundary is that of AdS_5 with logarithmic corrections reflecting the asymptotic freedom of QCD. We find that all relevant confining backgrounds have an IR singularity of the "good" kind that allows unambiguous spectrum computations. Near the singularity the 't Hooft coupling is driven to infinity. Asymptotically linear glueball masses can also be achieved. The classification of all confining asymptotics, the associated glueball spectra and meson dynamics are addressed in a companion paper, ArXiv:0707.1349

Paper Structure

This paper contains 35 sections, 253 equations, 9 figures.

Table of Contents

  1. Introduction and conclusions
  2. Motivating the gravitational dual of a large-N$_c$ gauge theory
  3. The spectrum
  4. The associated branes
  5. The effective action
  6. Holographic large N$_c$ YM: the vacuum structure
  7. General geometry and the geometric invariants
  8. The phase variable $X$ and the $\beta$-function
  9. Asymptotics of the geometry
  10. Asymptotic freedom and the UV geometry
  11. The $\alpha'$ corrections
  12. The UV geometry
  13. Confinement and the IR geometry
  14. Examples of background geometries
  15. Standard QCD type two-loop $\beta$-function
  16. ...and 20 more sections

Figures (9)

  • Figure 1: Dilaton potential as a function of $\lambda$ for the solution studied in section \ref{['twoloop']}.
  • Figure 2: The running of the coupling constant. It diverges at $u_0$.
  • Figure 3: Dilaton potential as a function of $\lambda$ when there is an IR fixed point. We have set $V_0=b_0=b_1=1$ for simplicity.
  • Figure 4: Running of the coupling constant in the Banks-Zaks case. We have set $V_0=b_0=b_1=1$.
  • Figure 5: Left:The dilaton potential plotted as a function of the t 'Hooft coupling for $x=5$. Right: The value of the t 'Hooft coupling at the extremum as a function of $x$.
  • ...and 4 more figures