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 zero-dimensional replica field theories belonging to the broadly interpreted "beta=2" Dyson symmetry class. We then utilise 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.

4.3 pages; final version to appear in PRL

References in corpus (18)

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• Replica treatment of non-Hermitian disordered Hamiltonians
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Cited by in corpus (17)

• Tau-Function Theory of Quantum Chaotic Transport with beta=1,2,4
• Integrable theory of quantum transport in chaotic cavities
• Superbosonization formula and its application to random matrix theory
• Statistics of thermal to shot noise crossover in chaotic cavities
• Equivalence of replica and cavity methods for computing spectra of sparse random matrices
• Correlations of RMT Characteristic Polynomials and Integrability: Hermitean Matrices
• Gaussian unitary ensembles with pole singularities near the soft edge and a system of coupled Painlevé XXXIV equations
• Non-differentiability of the effective potential and the replica symmetry breaking in the random energy model
• Painlevé III asymptotics of Hankel determinants for a singularly perturbed Laguerre weight
• The gradient flow of the Dirac spectrum
• On a distinguished family of random variables and Painlevé equations
• Random matrix ensembles with singularities and a hierarchy of Painlevé III equations
• Integrability of zero-dimensional replica field theories at beta=1
• Hankel determinants for a singular complex weight and the first and third Painlevé transcendents
• Hankel determinants for a perturbed Laguerre weight and Painleve V equation
• Critical edge behavior in the perturbed Laguerre ensemble and the Painleve V transcendent
• Single-use MIMO system, Painlevé transcendents and double scaling