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It has recently been demonstrated in quenched lattice simulations that the distribution of the low-lying eigenvalues of the QCD Dirac operator is universal and described by random-matrix theory. We present first evidence that this…
We discuss how the $1/N_c$ expansion and the chiral random matrix theory ($\chi$RMT) can be used in the study of large-$N_c$ gauge theories. We first clarify the parameter region in which each of these two approaches is valid: while the…
Motivated by recent progress on the understanding of the Eguchi-Kawai (EK) volume equivalence and growing interest in conformal window, we simultaneously use the large-Nc volume reduction and Chiral Random Matrix Theory (chRMT) to study the…
We introduce a random two-matrix model interpolating between a chiral Hermitian (2n+nu)x(2n+nu) matrix and a second Hermitian matrix without symmetries. These are taken from the chiral Gaussian Unitary Ensemble (chGUE) and Gaussian Unitary…
Massive spectral sum rules are derived for Dirac operators of $SU(N_c)$ gauge theories with $N_f$ flavors. The universal microscopic massive spectral densities of random matrix theory, where known, are all consistent with these sum rules.
Many evidences from lattice simulations support the idea that SU(2) with two Dirac flavors in the adjoint representation (also called Minimal Walking Technicolor) is IR conformal. A possible way to see this is through the behavior of the…
We derive the microscopic spectral density of the Dirac operator in $SU(N_c\geq 3)$ Yang-Mills theory coupled to $N_f$ fermions in the fundamental representation. An essential technical ingredient is an exact rewriting of this density in…
The emergence of the concept of a causal fermion system is revisited and further investigated for the vacuum Dirac equation in Minkowski space. After a brief recap of the Dirac equation and its solution space, in order to allow for the…
We present new results on chiral symmetry breaking in nearly conformal gauge theories with fermions in the fundamental representation of the SU(3) color gauge group. The number of fermion flavors is varied in an extended range below the…
Using the fermionic basis discovered in the 6-vertex model, we derive exact formulas for the expectation values of local operators of the sine-Gordon theory in any eigenstate of the Hamiltonian. We tested our formulas in the pure…
We construct a random matrix model that, in the large $N$ limit, reduces to the low energy limit of the QCD partition function put forward by Leutwyler and Smilga. This equivalence holds for an arbitrary number of flavors and any value of…
A systematic analysis of the genus two vacuum amplitudes of chiral self-dual conformal field theories is performed. It is explained that the existence of a modular invariant genus two partition function implies infinitely many relations…
We investigate spontaneous chiral symmetry breaking in SU(N) gauge theories at large N using overlap fermions. The exact zero modes and the low-lying modes of the Dirac operator provide the tools to gain insight into the interplay between…
We calculate the partition function of partially quenched chiral perturbation theory in the epsilon regime at next-to-leading order using the supersymmetry method in the formulation without a singlet particle. We include a nonzero imaginary…
We compute the partition function for the $N=1$ spinning particle, including pictures and the large Hilbert space, and show that it counts the dimension of the BRST cohomology in two- and four-dimensional target space. We also construct a…
We investigate the impact of finite volume effects on the critical number of flavours, N_f^c, for chiral symmetry restoration in QED3. To this end we solve a set of coupled Dyson-Schwinger equations on a torus. For order parameters such as…
A chiral random matrix model with complex eigenvalues is solved as an effective model for QCD with non-vanishing chemical potential. We derive new matrix model correlation functions which predict the local fluctuations of complex Dirac…
I derive constraints on the Dirac spectrum in the chirally symmetric phase of a gauge theory with two massless fermion flavors. Using only general properties of correlation functions of scalar and pseudoscalar bilinears, I prove that in the…
In this paper we give an unified approach to some questions arising in different fields of nonlinear analysis, namely: (a) the study of the structure of the Fu\v{c}\'\i k spectrum and (b) possible variants and extensions of the monotonicity…
The semiclassical approximation for the partition function in Chern-Simons gauge theory is derived using the invariant integration method. Volume and scale factors which were undetermined and had to be fixed by hand in previous derivations…