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F. Basile and G. Akemann JHEP12(2007)043 doi:10.1088/1126-6708/2007/12/043

Equivalence of QCD in the epsilon-regime and chiral random matrix theory with or without chemical potential

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F. Basile1,2 and G. Akemann1,3

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[1]
E.V. Shuryak and J.J.M. Verbaarschot, Random matrix theory and spectral sum rules for the Dirac operator in QCD 1993 Nucl. Phys. A 560 306 [hep-th/9212088]
CrossRef  Preprint 
[2]
J.J.M. Verbaarschot and T. Wettig, Random matrix theory and chiral symmetry in QCD 2000 Ann. Rev. Nucl. Part. Sci. 50 343 [hep-ph/0003017]
CrossRef  Preprint 
[3]
G. Akemann, Matrix models and QCD with chemical potential 2007 Int. J. Mod. Phys. A 22 1077 [hep-th/0701175]
CrossRef  Preprint 
[4]
J.J.M. Verbaarschot, The spectrum of the QCD Dirac operator and chiral random matrix theory: the threefold way 1994 Phys. Rev. Lett. 72 2531 [hep-th/9401059]
CrossRef  Preprint  PubMed 
[5]
A. Smilga and J.J.M. Verbaarschot, Spectral sum rules and finite volume partition function in gauge theories with real and pseudoreal fermions 1995 Phys. Rev. D 51 829 [hep-th/9404031]
CrossRef  Preprint 
[6]
D. Toublan and J.J.M. Verbaarschot, The spectral density of the QCD Dirac operator and patterns of chiral symmetry breaking 1999 Nucl. Phys. B 560 259 [hep-th/9904199]
CrossRef  Preprint 
[7]
J.C. Osborn, Universal results from an alternate random matrix model for QCD with a baryon chemical potential 2004 Phys. Rev. Lett. 93 222001 [hep-th/0403131]
CrossRef  Preprint  PubMed 
[8]
G. Akemann, P.H. Damgaard, J.C. Osborn and K. Splittorff, A new chiral two-matrix theory for Dirac spectra with imaginary chemical potential 2007 Nucl. Phys. B 766 34 [hep-th/0609059]
CrossRef  Preprint 
[9]
M.A. Stephanov, Random matrix model of QCD at finite density and the nature of the quenched limit 1996 Phys. Rev. Lett. 76 4472 [hep-lat/9604003]
CrossRef  Preprint  PubMed 
[10]
P. Littelmann, H.-J. Sommers and M.R. Zirnbauer, Superbosonization of invariant random matrix ensembles [0707.2929]
Preprint 
[11]
J.E. Bunder, K.B. Efetov, V.E. Kravtsov, O.M. Yevtushenko and M.R. Zirnbauer, Superbosonization formula and its application to random matrix theory [0707.2932]
Preprint 
[12]
T. Guhr, A. Müller-Groeling and H.A. Weidenmüller, Random matrix theories in quantum physics: common concepts 1998 Phys. Rep. 299 189 [cond-mat/9707301]
CrossRef  Preprint 
[13]
M.L. Mehta, Random matrices Third Edition, (Academic Press, London) U.K. (2004)

[14]
K. Splittorff and J.J.M. Verbaarschot, Replica limit of the Toda lattice equation 2003 Phys. Rev. Lett. 90 041601 [cond-mat/0209594]
CrossRef  Preprint  PubMed 
[15]
Y.V. Fyodorov and G. Akemann, On the supersymmetric partition function in QCD inspired random matrix models 2003 Sov. Phys. JETP Lett. 77 438 [2003 Pisma Zh. Eksp. Teor. Fiz. 77 513] [cond-mat/0210647]
CrossRef  Preprint 
[16]
G. Akemann, J.C. Osborn, K. Splittorff and J.J.M. Verbaarschot, Unquenched QCD Dirac operator spectra at nonzero baryon chemical potential 2005 Nucl. Phys. B 712 287 [hep-th/0411030]
CrossRef  Preprint 
[17]
K. Splittorff and J.J.M. Verbaarschot, QCD with bosonic quarks at nonzero chemical potential 2006 Nucl. Phys. B 757 259 [hep-th/0605143]
CrossRef  Preprint 
[18]
G. Akemann, P.H. Damgaard, U. Magnea and S. Nishigaki, Universality of random matrices in the microscopic limit and the Dirac operator spectrum 1997 Nucl. Phys. B 487 721 [hep-th/9609174]
CrossRef  Preprint 
[19]
P.H. Damgaard and S.M. Nishigaki, Universal spectral correlators and massive Dirac operators 1998 Nucl. Phys. B 518 495 [hep-th/9711023]
CrossRef  Preprint 
[20]
T. Wilke, T. Guhr and T. Wettig, The microscopic spectrum of the QCD Dirac operator with finite quark masses, 1998 Phys. Rev. D 57 6486 [hep-th/9711057]
CrossRef  Preprint 
[21]
S.M. Nishigaki, P.H. Damgaard and T. Wettig, Smallest Dirac eigenvalue distribution from random matrix theory 1998 Phys. Rev. D 58 087704 [hep-th/9803007]
CrossRef  Preprint 
 
P.H. Damgaard and S.M. Nishigaki, Distribution of the k-th smallest Dirac operator eigenvalue 2001 Phys. Rev. D 63 045012 [hep-th/0006111]
CrossRef  Preprint 
[22]
G. Akemann, J. Bloch, L. Shifrin and T. Wettig, Distributions of individual Dirac eigenvalues for QCD at non-zero chemical potential: RMT predictions and lattice results PoS(Lattice 2007)224 [0711.0629]
Preprint 
[23]
G. Akemann and P. Damgaard, Determination of Fπ from distributions of Dirac operator eigenvalues with imaginary density, PoS(Lattice 2007)166 [0709.0484]
Preprint 
[24]
K. Splittorff and J.J.M. Verbaarschot, Factorization of correlation functions and the replica limit of the Toda lattice equation 2004 Nucl. Phys. B 683 467 [hep-th/0310271]
CrossRef  Preprint 
[25]
G. Akemann, Y.V. Fyodorov and G. Vernizzi, On matrix model partition functions for QCD with chemical potential 2004 Nucl. Phys. B 694 59 [hep-th/0404063]
CrossRef  Preprint 
[26]
J.C. Osborn, Partially quenched QCD with a chemical potential 2006 PoS(LAT2006)142 [hep-lat/0610016]
Preprint 
[27]
Y.V. Fyodorov, Negative moments of characteristic polynomials of random matrices: Ingham-Siegel integral as an alternative to Hubbard-Stratonovich transformation 2002 Nucl. Phys. B 621 643 [math-ph/0106006]
CrossRef  Preprint 
[28]
J.C. Osborn, D. Toublan and J.J.M. Verbaarschot, From chiral random matrix theory to chiral perturbation theory 1999 Nucl. Phys. B 540 317 [hep-th/9806110]
CrossRef  Preprint 
[29]
P.H. Damgaard, J.C. Osborn, D. Toublan and J.J.M. Verbaarschot, The microscopic spectral density of the QCD Dirac operator 1999 Nucl. Phys. B 547 305 [hep-th/9811212]
CrossRef  Preprint 
[30]
D. Toublan and J.J.M. Verbaarschot, Statistical properties of the spectrum of the QCD Dirac operator at low energy 2001 Nucl. Phys. B 603 343 [hep-th/0012144]
CrossRef  Preprint 
[31]
P.H. Damgaard, U.M. Heller, K. Splittorff and B. Svetitsky, A new method for determining Fπ on the lattice, 2005 Phys. Rev. D 72 091501 [hep-lat/0508029]
CrossRef  Preprint 
 
P.H. Damgaard, U.M. Heller, K. Splittorff, B. Svetitsky and D. Toublan, Extracting Fπ from small lattices: unquenched results, 2006 Phys. Rev. D 73 074023 [hep-lat/0602030]
CrossRef  Preprint 
 
P.H. Damgaard, U.M. Heller, K. Splittorff, B. Svetitsky and D. Toublan, Microscopic eigenvalue correlations in QCD with imaginary isospin chemical potential 2006 Phys. Rev. D 73 105016 [hep-th/0604054]
CrossRef  Preprint 
[32]
G. Akemann and P.H. Damgaard, Distributions of Dirac operator eigenvalues 2004 Phys. Lett. B 583 199 [hep-th/0311171]
CrossRef  Preprint 
[33]
E. Kanzieper and V. Freilikher, Random matrix models with log-singular level confinement: method of fictitious fermions 1998 Philos. Mag. B 77 1161 [cond-mat/9704149]
Preprint 
 
A.B.J. Kuijlaars and M. Vanlessen, Universality for eigenvalue correlations at the origin of the spectrum 2003 Comm. Math. Phys. 243 163 [math-ph/0305044]
CrossRef  Preprint 
[34]
R.J. Szabo, Microscopic spectrum of the QCD Dirac operator in three dimensions 2001 Nucl. Phys. B 598 309 [hep-th/0009237]
CrossRef  Preprint 
[35]
J.J.M. Verbaarschot, QCD, chiral random matrix theory and integrability [hep-th/0502029]
Preprint 
[36]
N.I. Muskhelishvili, Singular integral equations Groningen, Noordhoff Netherlands (1953)

[37]
D. Toublan and J.J.M. Verbaarschot, Effective low energy theories and QCD Dirac spectra 2001 Int. J. Mod. Phys. B 15 1404 [hep-th/0001110]
CrossRef  Preprint 
[38]
Y.V. Fyodorov and H.-J. Sommers, Statistics of resonance widths in few channel chaotic scattering: crossover from isolated to overlapping resonances 1996 Sov. Phys. JETP Lett. 63 1026 [cond-mat/9507117]
CrossRef  Preprint 
[39]
J.J.M. Verbaarschot, The supersymmetric method in random matrix theory and applications to QCD 2005 AIP Conf. Proc. 744 277 [hep-th/0410211]
CrossRef  Preprint 
[40]
D. Dalmazi and J.J.M. Verbaarschot, The replica limit of unitary matrix integrals 2001 Nucl. Phys. B 592 419 [hep-th/0005229]
CrossRef  Preprint 
[41]
H. Leutwyler and A. Smilga, Spectrum of Dirac operator and role of winding number in QCD 1992 Phys. Rev. D 46 5607
CrossRef 
[42]
M.R. Zirnbauer, Riemannian symmetric superspaces and their origin in random-matrix theory 1996 J. Math. Phys. 37 4986 [math-ph/9808012]
CrossRef  Preprint 
[43]
A.V. Andreev, B.D. Simons and N. Taniguchi, Supersymmetry applied to the spectrum edge of random matrix ensembles 1994 Nucl. Phys. B 432 487
CrossRef 
[44]
Y.V. Fyodorov, B.A. Khoruzhenko and H.-J. Sommers, Almost-hermitian random matrices: eigenvalue density in the complex plane 1997 1997 Phys. Lett. A 226 46 [cond-mat/9606173]
CrossRef  Preprint 
 
M.R. Zirnbauer, Almost-hermitian random matrices: crossover from Wigner-Dyson to Ginibre eigenvalue statistics Phys. Rev. Lett. 79 557 [cond-mat/9703152]
Preprint 
[45]
J. Feinberg and A. Zee, Non-hermitian random matrix theory: method of hermitian reduction 1997 Nucl. Phys. B 504 579 [cond-mat/9703087]
CrossRef  Preprint 
[46]
R.A. Janik, M.A. Nowak, G. Papp and I. Zahed, Nonhermitean random matrix models. I 1997 Nucl. Phys. B 501 603 [cond-mat/9612240]
CrossRef  Preprint 
[47]
G. Akemann and A. Pottier, Ratios of characteristic polynomials in complex matrix models 2004 J. Phys. A: Math. Gen. 37 L453 [math-ph/0404068]
IOPscience  Preprint 
[48]
N. Kawamoto and J. Smit, Effective lagrangian and dynamical symmetry breaking in strongly coupled lattice QCD 1981 Nucl. Phys. B 192 100
CrossRef 
[49]
G. Hackenbroich and H.A. Weidenmüller, Universality of random-matrix results for non-gaussian ensembles 1995 Phys. Rev. Lett. 74 4118 [cond-mat/9412088]
CrossRef  Preprint  PubMed 
[50]
N. Lehmann, D. Saher, V.V. Sokolov and H.-J. Sommers, Chaotic scattering - the supersymmetry method for large number of channels 1995 Nucl. Phys. A 582 223

[51]
F. Berruto, R.C. Brower and B. Svetitsky, Effective Lagrangian for strongly coupled domain wall fermions 2001 Phys. Rev. D 64 114504 [hep-lat/0105016]
CrossRef  Preprint 
[52]
K.B. Efetov, G. Schwiete and K. Takahashi, Bosonization for disordered and chaotic systems 2004 Phys. Rev. Lett. 92 026807 [cond-mat/0307504]
CrossRef  Preprint  PubMed 
[53]
T. Guhr, Arbitrary rotation invariant random matrix ensembles and supersymmetry 2006 J. Phys. A 39 13191 [math-ph/0606014]
Preprint 
[54]
W. Rudin, Real and complex analysis (McGraw-Hill) (1970)

[55]
M.J. Rothstein, Integration on noncompact supermanifolds 1987 Trans. Am. Math. Soc. 299 387
CrossRef 
[56]
B. DeWitt, Supermanifolds (Cambridge University Press, Cambridge) U.K. (1984)

[57]
B. Schlittgen and T. Wettig, Generalizations of some integrals over the unitary group 2003 J. Phys. A: Math. Gen. 36 3195 [math-ph/0209030]
IOPscience  Preprint 
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