An Itzykson-Zuber-like Integral and Diffusion for Complex Ordinary and Supermatrices

We compute an analogue of the Itzykson-Zuber integral for the case of arbitrary complex matrices. The calculation is done for both ordinary and supermatrices by transferring the Itzykson-Zuber diffusion equation method to the space of arbitrary complex matrices. The integral is of interest for applications in Quantum Chromodynamics and the theory of two-dimensional Quantum Gravity.Comment: 20 pages, RevTeX, no figures, agrees with published version, including "Note added in proof" with an additional result for rectangular supermatrice

Bosonic color-flavor transformation for the special unitary group

We extend Zirnbauer's color-flavor transformation in the bosonic sector to the color group SU(N_c). Because the flavor group U(N_b, N_b) is non-compact, the algebraic method by which the original color-flavor transformation was derived leads to a useful result only for 2N_b \le N_c. Using the character expansion method, we obtain a different form of the transformation in the extended range N_b \le N_c. This result can also be used for the color group U(N_c). The integrals to which the transformation can be applied are of relevance for the recently proposed boson-induced lattice gauge theory.Comment: 34 pages, 2 figure

Dirac eigenvalue correlations in quenched QCD at finite density

We compare eigenvalue correlations of the Dirac operator with a chemical potential obtained from lattice simulations of quenched QCD with analytic predictions obtained from chiral effective theories in the zero-momentum limit. By comparing the density and two-point correlation function we show that the analytic results agree with QCD at low energies. We also examine the scale (Thouless energy) up to which the zero-momentum approximation is valid.Comment: 6 pages, 12 figures, talk given at Lattice 200

Banks-Casher-type relation for the BCS gap at high density

We derive a new Banks-Casher-type relation which relates the density of complex Dirac eigenvalues at the origin to the BCS gap of quarks at high density. Our relation is applicable to QCD and QCD-like theories without a sign problem, such as two-color QCD and adjoint QCD with baryon chemical potential, and QCD with isospin chemical potential. It provides us with a method to measure the BCS gap through the Dirac spectrum on the lattice.Comment: 14 pages, 2 figures, some additions (in particular eq. (4.13)), version to appear in EPJ