The Large $N_c$ limit of QCD on the lattice

Abstract

We review recent progress in the study of the large $N_c$ limit of gauge theories from lattice simulations. The focus is not only the planar limit but also the size of $\mathcal{O}(N_c^{-1})$ corrections for values of $N_c\gtrsim 3$. Some concrete examples of the topics we include are tests of large-$N_c$ factorization, the topological susceptibility, the glueball, meson and baryon spectra, the chiral dependence of masses and decay constants, and weak matrix elements related to the $\Delta I=1/2$ rule in kaon decays.

Contribution to the EPJA special issue "Lattice Field Theory during the COVID-19 pandemic". 19 pages, 17 figures, 1 table. Accepted in EPJA. Minor formatting issue fixed

References in corpus (29)

• SU(N) gauge theories at large N
• Critical slowing down and error analysis in lattice QCD simulations
• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Volume independence in large Nc QCD-like gauge theories
• Scalar mesons in a finite volume
• $K\to \pi \pi$ $\Delta I=3/2$ decay amplitude in the continuum limit
• UV Completions of Partial Compositeness: The Case for a SU(4) Gauge Group
• Glueball masses in the large N limit
• Continuum Thermodynamics of the GluoN_c Plasma
• The string tension from smeared Wilson loops at large N
• The pressure of the SU(N) lattice gauge theory at large-N
• Topological susceptibility and the sampling of field space in $N_f=2$ lattice QCD simulations
• $\theta$ dependence of 4D $SU(N)$ gauge theories in the large-$N$ limit
• Meson-meson Scattering in QCD-like Theories
• The topological susceptibility in the large-N limit of SU(N) Yang-Mills theory
• Large-$N_c$ naturalness in coupled-channel meson-meson scattering
• The perturbative QCD gradient flow to three loops
• Spectroscopy of SU(4) gauge theory with two flavors of sextet fermions
• On the running of the bare coupling in SU(N) lattice gauge theories
• Testing volume independence of SU(N) pure gauge theories at large N
• $\theta$-dependence and center symmetry in Yang-Mills theories
• Feynman-Hellmann theorem for resonances and the quest for QCD exotica
• The Nc dependencies of baryon masses: Analysis with Lattice QCD and Effective Theory
• The topological susceptibility of two-dimensional $U(N)$ gauge theories
• K-->pipi amplitudes from lattice QCD with a light charm quark
• The vector meson mass in the large N limit of QCD
• The flavor dependence of $m_{\varrho }/f_{\pi }$
• Non-leptonic kaon decays at large $N_c$
• Topological susceptibility in QCD with two flavors and 3-5 colors -- a pilot study