Large-Nc gauge theory and chiral random matrix theory
Volume
88
Pagination
025046 - ?
Publisher
DOI
10.1103/physrevd.88.025046
Journal
Physical Review D
Issue
ISSN
2470-0010
Metadata
Show full item recordAbstract
We discuss how the 1/𝑁𝑐 expansion and the chiral random matrix theory (𝜒RMT) 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 𝜒RMT. 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 𝜒RMT with some care. 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 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(𝑁𝑐) gauge theory in the large-𝑁𝑐 and the large-volume limit and therefore supports the validity of the combined approach. We also provide an interpretation of the gap and unexpected 𝑁𝑐 scaling, both of which are observed in the Dirac spectrum.
Authors
Hanada, M; Lee, J-W; Yamada, NCollections
- Mathematics [1686]