Domain-wall induced quark masses in topologically nontrivial backgrounds

In the domain-wall formulation of chiral fermions, the finite separation between domain walls (Lₛ) induces an effective quark mass (meff) which complicates the chiral limit. In this work, we study the size of the effective mass as a function of Lₛ and the domain-wall height m₀ by calculating the smallest eigenvalue of the Hermitian domain-wall Dirac operator in the topologically nontrivial background fields. We find that, just as in the free case, meff decreases exponentially in Lₛ with a rate depending on m₀. However, quantum fluctuations amplify the wall effects significantly. Our numerical result is consistent with a previous study of the effective mass from the Gell-Mann--Oakes--Renner relation.