Large-N-c gauge theory and chiral random matrix theory

作者：Hanada Masanori^*; Lee Jong Wan; Yamada Norikazu

来源：Physical Review D - Particles, Fields, Gravitation and Cosmology, 2013, 88(2): 025046.

DOI：10.1103/PhysRevD.88.025046

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 (%26apos;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 care. 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 overlap-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 an interpretation of the gap and unexpected N-c scaling, both of which are observed in the Dirac spectrum.

• 出版日期2013-7-26