Large-Nc gauge theory and chiral random matrix theory
Abstract
We discuss how the 1/Nc expansion and the chiral random matrix theory () can be used in the study of large-Nc 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-Nc arguments ('t Hooft large-Nc limit), m must be scaled appropriately with a certain negative power of Nc in order for the gauge theories to be described by the . 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-Nc argument and the with some cares. As a concrete example, we numerically study the four dimensional SU(Nc) gauge theory with Nf=2 heavy adjoint fermions, introduced as the center symmetry preserver keeping the infrared physics intact, on a 24 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(Nc) gauge theory in the large-Nc and the large-volume limit, and therefore supports the validity of the combined approach. We also provide the interpretation of the gap and unexpected Nc-scaling, both of which are observed in the Dirac spectrum.