Large-$N_c$ gauge theory and chiral random matrix theory

Abstract

We discuss how the $1/N_c$ expansion and the chiral random matrix theory ($\chi$RMT) can be used in the study of large-$N_c$ gauge theories. We first clarify the parameter region in which each of these two approaches is valid: while the fermion mass $m$ is fixed in the standard large-$N_c$ arguments ('t Hooft large-$N_c$ limit), $m$ must be scaled appropriately with a certain negative power of $N_c$ in order for the gauge theories to be described by the $\chi$RMT. Then, although these two limits are not compatible in general, we show that the breakdown of chiral symmetry can be detected by combining the large-$N_c$ argument and the $\chi$RMT with some cares. As a concrete example, we numerically study the four dimensional $SU(N_c)$ gauge theory with $N_f=2$ heavy adjoint fermions, introduced as the center symmetry preserver keeping the infrared physics intact, on a $2^4$ lattice. By looking at the low-lying eigenvalues of the Dirac operator for a massless probe fermion in the adjoint representation, we find that the chiral symmetry is indeed broken with the expected breaking pattern. This result reproduces a well-known fact that the chiral symmetry is spontaneously broken in the pure $SU(N_c)$ gauge theory in the large-$N_c$ and the large-volume limit, and therefore supports the validity of the combined approach. We also provide the interpretation of the gap and unexpected $N_c$-scaling, both of which are observed in the Dirac spectrum.

26 pages, 15 figures

References in corpus (16)

• SU(N) gauge theories at large N
• Center-stabilized Yang-Mills theory: confinement and large $N$ volume independence
• Volume independence in large Nc QCD-like gauge theories
• Abelian duality, confinement, and chiral symmetry breaking in QCD(adj)
• Two-flavor lattice QCD simulation in the epsilon-regime with exact chiral symmetry
• Two-flavor QCD simulation with exact chiral symmetry
• Matrix Models and QCD with Chemical Potential
• Symmetry Breaking In Twisted Eguchi-Kawai Models
• Lattice study of two-dimensional N=(2,2) super Yang-Mills at large-N
• Large-N reduction in QCD-like theories with massive adjoint fermions
• Orbifold equivalence and the sign problem at finite baryon density
• Phase structure of twisted Eguchi-Kawai model
• Breakdown of large-N quenched reduction in SU(N) lattice gauge theories
• No-Go Theorem for Critical Phenomena in Large-Nc QCD
• Numerical computation of the beta function of large N SU(N) gauge theory coupled to an adjoint Dirac fermion
• Chiral Dynamics With Wilson Fermions

Cited by in corpus (1)

• Introductory lectures to large-N QCD phenomenology and lattice results