The $ϵ$-regime of dilaton chiral perturbation theory

The $ϵ$-regime of dilaton chiral perturbation theory is introduced. We compute the dilaton mass, the chiral condensate and the topological susceptibility in the $ϵ$-regime, as a function of the fermion mass. The microscopic spectral density of the Dirac operator is obtained from dilaton chiral perturbation theory. Our main result is that the chiral condensate and the spectral density are related to their counterparts from ordinary chiral perturbation theory via a simple scaling relation. This relation originates from the mass dependence of the dilaton potential, and is valid in both the $ϵ$-regime and the $p$-regime. In the $ϵ$-regime, moreover, all results agree with the universal predictions to leading order in $ϵ$.