Exact beta function from the holographic loop equation of large-N QCD_4

Abstract

We construct and study a previously defined quantum holographic effective action whose critical equation implies the holographic loop equation of large-N QCD_4 for planar self-avoiding loops in a certain regularization scheme. We extract from the effective action the exact beta function in the given scheme. For the Wilsonean coupling constant the beta function is exacly one loop and the first coefficient agrees with its value in perturbation theory. For the canonical coupling constant the exact beta function has a NSVZ form and the first two coefficients agree with their value in perturbation theory.

42 pages, latex. The exponent of the Vandermonde determinant in the quantum effective action has been changed, because it has been employed a holomorphic rather than a hermitean resolution of identity in the functional integral. Beta function unchanged. New explanations and references added, typos corrected

References in corpus (28)

• Supersymmetric Yang-Mills Systems And Integrable Systems
• Wilson Loops and Minimal Surfaces
• Chiral Rings and Anomalies in Supersymmetric Gauge Theory
• A Perturbative Window into Non-Perturbative Physics
• Large $N$ Phase Transition in Continuum QCD${}_2$
• Mirror symmetry, Langlands duality, and the Hitchin system
• The wall of the cave
• Moduli Space of Non-Abelian Vortices
• Holomorphy, Rescaling Anomalies and Exact beta Functions in Supersymmetric Gauge Theories
• Exact Results in Non-Supersymmetric Large N Orientifold Field Theories
• SUSY Relics in One-Flavor QCD from a New 1/N Expansion
• Mastering the Master Field
• Moduli Spaces of Parabolic Higgs Bundles and Parabolic K(D) Pairs over Smooth Curves: I
• Hitchin-Kobayashi correspondence, quivers, and vortices
• Refining the Proof of Planar Equivalence
• Holomorphic matrix models
• Stochastic Master Fields
• (Anti)symmetric matter and superpotentials from IIB orientifolds
• Wilson loop for large N Yang-Mills theory on a two-dimensional sphere
• Two dimensional QCD is a one dimensional Kazakov-Migdal model
• Exact Results in Gauge Theories: Putting Supersymmetry to Work. The 1999 Sakurai Prize Lecture
• Wild nonabelian Hodge theory on curves
• Large N Gauge Theory -- Expansions and Transitions
• Decorated Teichmüller Theory of Bordered Surfaces
• The large-N limit of QCD and the collective field of the Hitchin fibration
• Solving loop equations by Hitchin systems via holography in large-N QCD_4
• Joining-splitting interaction of non-critical string
• Twisted local systems solve the (holographic) loop equation of large-N QCD_4

Cited by in corpus (4)

• Supersymmetry Inspired QCD Beta Function
• Dynamical Stabilization of the Fermi Scale: Phase Diagram of Strongly Coupled Theories for (Minimal) Walking Technicolor and Unparticles
• Quasi BPS Wilson loops, localization of loop equation by homology and exact beta function in the large N limit of SU(N) Yang-Mills theory
• A Linear Equation for Wilson Loops