# A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential

Akemann G, Damgaard PH, Osborn JC, Splittorff K (2007)
Nucl.Phys.B 766(1-3): 34-67.

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Abstract
We solve a new chiral Random Two-Matrix Theory by means of biorthogonalpolynomials for any matrix size $N$. By deriving the relevant kernels we findexplicit formulas for all $(n,k)$-point spectral (mixed or unmixed) correlationfunctions. In the microscopic limit we find the corresponding scalingfunctions, and thus derive all spectral correlators in this limit as well. Weextend these results to the ordinary (non-chiral) ensembles, and also thereprovide explicit solutions for any finite size $N$, and in the microscopicscaling limit. Our results give the general analytical expressions for themicroscopic correlation functions of the Dirac operator eigenvalues in theorieswith imaginary baryon and isospin chemical potential, and can be used toextract the tree-level pion decay constant from lattice gauge theoryconfigurations. We find exact agreement with previous computations based on thelow-energy effective field theory in the two special cases where comparisonsare possible.
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Akemann G, Damgaard PH, Osborn JC, Splittorff K. A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential. Nucl.Phys.B. 2007;766(1-3):34-67.
Akemann, G., Damgaard, P. H., Osborn, J. C., & Splittorff, K. (2007). A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential. Nucl.Phys.B, 766(1-3), 34-67. doi:10.1016/j.nuclphysb.2006.12.016
Akemann, G., Damgaard, P. H., Osborn, J. C., and Splittorff, K. (2007). A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential. Nucl.Phys.B 766, 34-67.
Akemann, G., et al., 2007. A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential. Nucl.Phys.B, 766(1-3), p 34-67.
G. Akemann, et al., “A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential”, Nucl.Phys.B, vol. 766, 2007, pp. 34-67.
Akemann, G., Damgaard, P.H., Osborn, J.C., Splittorff, K.: A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential. Nucl.Phys.B. 766, 34-67 (2007).
Akemann, Gernot, Damgaard, P. H., Osborn, J. C., and Splittorff, K. “A new Chiral Two-Matrix Theory for Dirac Spectra with Imaginary Chemical Potential”. Nucl.Phys.B 766.1-3 (2007): 34-67.
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arXiv hep-th/0609059