Topology and pion correlators — a study in the Nf = 2 Schwinger model

Abstract

I readdress the issue whether the topological charge of the gauge background has an influence on a hadronic observable. To this end pion correlators in the Schwinger model with 2 dynamical flavours are determined on subensembles with a fixed topological charge. It turns out that the answer depends on a specific function of the sea-quark mass and the box volume which is in close analogy to the Leutwyler-Smilga parameter in full QCD.

Sum rules for the Dirac spectrum of the Schwinger model

“…Leutwyler-Smilga sum rules have been obtained both for zero and nonzero topological charge [10]. The distributions of the smallest eigenvalues of the Dirac operator for the Schwinger model [7,10,17,18] agree with analytical results obtained by means of chiral Lagrangians [20,26] and random matrix theory [24,25,32].…”

“…Analytical results obtained for the Schwinger model have been tested elaborately by means of Monte-Carlo simulations. The numerical value of the chiral condensate has been reproduced accurately [7,17,18]. The index theorem was confirmed and the fermionic would-be zero modes were identified [9,10].…”

“…For nonperturbative phenomena, two approaches which both have been tested in the Schwinger model, have been very successful: lattice simulations and chiral perturbation theory. In particular, a large number of lattice studies have benefited from the Schwinger model [5,6,7,8,9,10,11,12,13,14,15,16,17,18]. Among others, we mention the study of chiral fermions on the lattice [8,9,10,14], the analysis of the continuum limit for staggered fermions [17], and the effect of quenching on the Dirac spectrum [18,19].…”

“…In particular, a large number of lattice studies have benefited from the Schwinger model [5,6,7,8,9,10,11,12,13,14,15,16,17,18]. Among others, we mention the study of chiral fermions on the lattice [8,9,10,14], the analysis of the continuum limit for staggered fermions [17], and the effect of quenching on the Dirac spectrum [18,19].…”

Lattice study of the massive Schwinger model with aθterm under Lüscher’s “admissibility” condition

“…A related but somewhat different approach was proposed by Dürr [37] where one makes a quenched calculation and give the whole fermion determinant as the reweighting factor. He also proposed an approximation in which one replaces the determinant for the given configuration by the determinant of a common representative configuration for the given sector, which reduces the enormous computational effort .…”