Banks-Casher Relation Research Articles

The low-lying Dirac eigenmodes from domain wall fermions

We calculate the low-lying eigenvalues and eigenvectors of the hermitian domain wall Dirac operator on various gauge backgrounds by Ritz minimization. The mass dependence of these eigenvalues is studied to extract the physical 4 dimensional λ, whose spectral density is related to 〈 ψ ψ〉 through the Banks-Casher relation, and δ m, which represents the effects of the residual chiral symmetry breaking in domain wall formalism on a per eigenmode basis. The topological structure of the underlying gauge field is examined by measuring the Γ 5 matrix elements between the low-lying eigenmodes.

On a Banks-Casher relation in MQCD

We discuss the meaning of a Banks–Casher relation for the Dirac operator eigenvalues in MQCD. It is argued that the eigenvalue can be identified with a coordinate involved in the string compactification manifold.