2004/10/25 by T. Andersson, T. and Andersson, P. H. Damgaard +2
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Correlation function (quantum field theory) #Generating function #Integrable system #Lattice (music) #Lattice QCD #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Partition function (quantum field theory) #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Replica #Sign (mathematics) #Spectral function #Statistical physics #Theoretical and Computational Physics #Toda lattice #hep-th
paper · pdf · doi:10.1016/j.nuclphysb.2004.11.051
published as Nucl.Phys. B707 (2005) 509-528 · 18 pages, 2 figures
arxiv created 2004/10/25 · openalex publication_date 2004/12/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the epsilon-regime of QCD in 3 dimensions. It is shown that the leading term of the effective partition function satisfies a set of Toda lattice equations, recursive in the number of flavors. Taking the replica limit of these Toda equations allows us to derive the microscopic spectral correlation functions for the QCD Dirac operator in 3 dimensions. For an even number of flavors we reproduce known results derived using other techniques. In the case of an odd number of flavors the theory has a severe sign problem, and we obtain previously unknown microscopic spectral correlation functions.