Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-09-08
Nucl.Phys.B766:34-67,2007; Erratum-ibid.B800:406-407,2008
Physics
High Energy Physics
High Energy Physics - Theory
31 pages 2 figures, v2 missing term in partially quenched results inserted, fig 2 updated
Scientific paper
10.1016/j.nuclphysb.2006.12.016
We solve a new chiral Random Two-Matrix Theory by means of biorthogonal polynomials for any matrix size $N$. By deriving the relevant kernels we find explicit formulas for all $(n,k)$-point spectral (mixed or unmixed) correlation functions. In the microscopic limit we find the corresponding scaling functions, and thus derive all spectral correlators in this limit as well. We extend these results to the ordinary (non-chiral) ensembles, and also there provide explicit solutions for any finite size $N$, and in the microscopic scaling limit. Our results give the general analytical expressions for the microscopic correlation functions of the Dirac operator eigenvalues in theories with imaginary baryon and isospin chemical potential, and can be used to extract the tree-level pion decay constant from lattice gauge theory configurations. We find exact agreement with previous computations based on the low-energy effective field theory in the two special cases where comparisons are possible.
Akemann Gernot
Damgaard Poul H.
Osborn James C.
Splittorff Kim
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