Related papers: Chiral Random Matrix Models in QCD

These lecture notes include the following topics. Chapter 1 deals with QCD and its global symmetries in the chiral limit, explicit symmetry breaking in terms of the quark masses, and the concept of Green functions and Ward identities…

In this lecture we discuss various aspects of QCD at nonzero chemical potential, including its phase diagram and the Dirac spectrum, and summarize what chiral random matrix theory has contributed to this subject. To illustrate the…

The physical origin of the strong CP problem in QCD, rooted in the structures of the vacuum of the standard model, is reviewed. The chiral solution to this problem, with its accompanying axion, is explained and various characteristics of…

Quasi-Monte Carlo (QMC) methods for estimating integrals are attractive since the resulting estimators typically converge at a faster rate than pseudo-random Monte Carlo. However, they can be difficult to set up on arbitrary posterior…

The construction of the effective Lagrangian relevant for the mesonic sector of QCD in the large N_c limit meets with a few rather subtle problems. We thoroughly examine these and show that, if the variables of the effective theory are…

We consider a lattice-inspired random matrix model for the QCD chiral phase transition at finite chemical potential. Useful features of the usual RMM for QCD at finite chemical potential are reobtained, some being brought closer to their…

In a deep-infrared (ergodic) regime, QCD coupled to massive pseudoreal and real quarks are described by chiral orthogonal and symplectic ensembles of random matrices. Using this correspondence, general expressions for the QCD partition…

We summarise recent results for the chiral Random Two-Matrix Theory constructed to describe QCD in the epsilon-regime with imaginary chemical potential. The virtue of this theory is that unquenched Lattice simulations can be used to…

Exact results from random matrix theory are used to systematically analyse the relationship between microscopic Dirac spectra and finite-volume partition functions. Results are presented for the unitary ensemble, and the chiral analogs of…

In these lectures I explain how chiral symmetry of continuum QCD naturally leads to a class of lattice regularisations known as twisted mass QCD (tmQCD). As compared to standard Wilson quarks, its advantages are the absence of unphysical…

We describe a rearrangement of the standard expansion of the symmetry breaking part of the QCD effective Lagrangian that includes into each order additional terms which in the standard chiral perturbation theory ($\chi$PT) are relegated to…

We characterize the maximal attainable power-size gap in overidentified instrumental variables models with heteroskedastic or autocorrelated (HAC) errors. Using total variation distance and Kraft's theorem, we define the decision theoretic…

Two flavour massless QCD has a second order chiral transition which has been argued to belong to the universality class of the $3d$ O(4) spin model. The arguments have been questioned recently, and the transition was claimed to be mean…

We revisit the gauge hierarchy problem with the emphasis on the chiral property of the Standard Model. We present a model realizing a gauge hierarchy. Along this line, we also comment briefly on the "very light" axions and the upper bound…

We introduce the concept of $\epsilon$-uncontrollability for random linear systems, i.e. linear system in which the usual matrices have been replaced by random matrices. We also estimate the $\epsilon$-uncontrollability in the case where…

We prove a universal limit theorem for the halting time, or iteration count, of the power/inverse power methods and the QR eigenvalue algorithm. Specifically, we analyze the required number of iterations to compute extreme eigenvalues of…

Recently, the Columbia group obtained the valence quark mass dependence of the chiral condensate for lattice QCD simulations with dynamical fermions for a series of couplings close to the critical temperature. In this letter we show that…

This talk first discusses some aspects of the chiral expansion with three light flavours related to the (non) applicability of the OZI rule. Next, the extension of ChPT to an effective theory of the full standard model is considered. Some…

The role of a chiral U(1) phase in the quark mass in QCD is analysed from first principles. In operator formulation, there is a parity symmetry and the phase can be removed by a change in the representation of the Dirac gamma matrices.…

We study the universal scaling limit of random partitions obeying the Schur measure. Extending our previous analysis [arXiv:2012.06424], we obtain the higher-order Pearcey kernel describing the multi-critical behavior in the cusp scaling…