Related papers: Partition function zeros in QCD
We reveal that the universal scaling properties of the chiral phase transition in quantum chromodynamics (QCD) at the macroscale are, in fact, encoded within the microscopic energy levels of its fundamental constituents, the quarks. We…
We study the interplay of quark number density and chiral symmetry in lattice QCD. We suggest that both are controlled by the eigenvalue spectrum of the fermionic propagator matrix, which shapes the pattern of zeros of the partition…
We present combinatorial and analytical results concerning a Sheffer sequence with a generating function of the form $G(x,z)=Q(z)^{x}Q(-z)^{1-x}$, where $Q$ is a quadratic polynomial with real zeros. By using the properties of Riordan…
We study a generalization of the Callan-Harvey mechanism to the case of a non local mass. Using a 2+1 model as a concrete example, we show that both the existence and properties of localized zero modes can also be consistently studied when…
We use the graded eigenvalue method, a variant of the supersymmetry technique, to compute the universal spectral correlations of the QCD Dirac operator in the presence of massive dynamical quarks. The calculation is done for the chiral…
Dyonic classical solutions of Yang-Mills theory are considered and the complete set of fermionic zero modes of these solutions are studied. Representing the QCD vacuum as a gas of dyons, one obtains chiral symmetry breaking due to zero…
The partition function of two dimensional QCD on a Riemann surface of area $A$ is expanded as a power series in $1/N$ and $A$. It is shown that the coefficients of this expansion are precisely determined by a sum over maps from a two…
We consider the parity-invariant Dirac operator with a mass term in three-dimensional QCD for $N_c=2$ and quarks in the fundamental representation. We show that there exists a basis in which the matrix elements of the Euclidean Dirac…
The partition function of a factor graph and the partition function of the dual factor graph are related to each other by the normal factor graph duality theorem. We apply this result to the classical problem of computing the partition…
We link the spontaneous breakdown of chiral symmetry in Euclidean QCD to the collision of spectral shock waves in the vicinity of zero eigenvalue of Dirac operator. The mechanism, originating from complex Burger's-like equation for viscid,…
We study in detail the zero set of a regular function of a quaternionic or octonionic variable. By means of a division lemma for convergent power series, we find the exact relation existing between the zeros of two octonionic regular…
We exploit transformations relating generalized $q$-series, infinite products, sums over integer partitions, and continued fractions, to find partition-theoretic formulas to compute the values of constants such as $\pi$, and to connect sums…
By matching 1/m^2 divergences in finite-volume two-point correlation functions of the scalar or pseudoscalar densities with those obtained in chiral perturbation theory, we derive a relation between the Dirac operator zero-mode…
We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum…
We show that integrable structure of chiral random matrix models incorporating global symmetries of QCD Dirac operators (labeled by the Dyson index beta=1,2, and 4) leads to emergence of a connection relation between the spectral statistics…
The properties of the spectrum of the overlap Dirac operator and their relation to random matrix theory are studied. In particular, the predictions from chiral random matrix theory in topologically non-trivial gauge field sectors are…
We describe the occurrence and physical role of zero-energy modes in the Dirac equation with a topologically non-trivial background.
Two different matrix models for QCD with a non-vanishing quark chemical potential are shown to be equivalent by mapping the corresponding partition functions. The equivalence holds in the phase with broken chiral symmetry. It is exact in…
We review some motivation behind the introduction of chiral random matrix models in QCD, with particular emphasis on the importance of the Gell-Mann-Oakes (GOR) relation for these arguments. We show why the microscopic limit is universal in…
We consider QCD_3 with an odd number of flavors in the mesoscopic scaling region where the field theory finite-volume partition function is equivalent to a random matrix theory partition function. We argue that the theory is parity…