Are Bosonic Replicas Faulty?

Abstract

Motivated by the ongoing discussion about a seeming asymmetry in the performance of fermionic and bosonic replicas, we present an exact, nonperturbative approach to both fermionic and bosonic zero-dimensional replica field theories belonging to the broadly interpreted beta=2 Dyson symmetry class. We then utilize the formalism developed to demonstrate that the bosonic replicas do correctly reproduce the microscopic spectral density in the QCD-inspired chiral Gaussian unitary ensemble. This disproves the myth that the bosonic replica field theories are intrinsically faulty.