Related papers: The Microscopic Spectral Density of the QCD Dirac …

Introduction of supersymmetry into the noncommutative geometry is investigated. We propose a new Dirac operator which plays the role of the metric over the extended algebra of chiral and antichiral supermultiplets and is invariant under the…

The Dirac operator for a manifold Q, and its chirality operator when Q is even dimensional, have a central role in noncommutative geometry. We systematically develop the theory of this operator when Q=G/H, where G and H are compact…

We consider 1+1 dimensional SU(N) gauge theory coupled to a multiplet of massive Dirac fermions transforming in the adjoint representation of the gauge group. The only global symmetry of this theory is a U(1) associated with the conserved…

We analytically study two-color QCD with an even number of flavors at high baryon density. This theory is free from the fermion sign problem. Chiral symmetry is broken spontaneously by the diquark condensate. Based on the symmetry breaking…

We calculate the spectral function of the QCD Dirac operator using the four-dimensional effective operator constructed from the Mobius domain-wall implementation. We utilize the eigenvalue filtering technique combined with the stochastic…

Random Matrix Theory has been a unifying approach in physics and mathematics.In these lectures we discuss applications of Random Matrix Theory to QCD and emphasize underlying integrable structures. In the first lecture we give an overview…

We study the eigenvalues of Dirac operators in QCD with two mass degenerate dynamical fermions. The gauge configurations have been obtained with HMC and the so-called Chirally Improved fermionic action. We compare eigenvalues obtained for…

Yangian symmetry of amplitudes in $\mathcal{N}=4$ super Yang-Mills theory is formulated in terms of eigenvalue relations for monodromy matrix operators. The Quantum Inverse Scattering Method provides the appropriate tools to treat the…

We study the singular values of the Dirac operator in dense QCD-like theories at zero temperature. The Dirac singular values are real and nonnegative at any nonzero quark density. The scale of their spectrum is set by the diquark…

We investigate the leading terms of the spectral action for odd-dimensional Riemannian spin manifolds with the Dirac operator perturbed by a scalar function. We calculate first two Gilkey-de Witt coefficients and make explicit calculations…

2d QCD, Yang-Mills theory with gauge group G and massless quarks in representations (R_\ell, R_r) of G, flows in the infrared to a CFT or a TQFT depending on whether spectrum is gapless or gapped. We identify the infrared effective theory…

The generating functional of heavy baryon chiral perturbation theory at order O(Q^2) in the mean field approximation (with a pseudoscalar source coupling which is consistent with the PCAC-Ward identities on the current quark level) has been…

We derive p+1-dimensional (p=1,2) maximally supersymmetric U(N) Yang-Mills theory from the wrapped supermembrane on $R^{11-p}\times T^{p}$ in the light-cone gauge by using the matrix regularization. The elements of the matrices in the super…

Super-Yang-Mills theory (SYM) is a central building block for supersymmetric extensions of the Standard Model of particle physics. Whereas the weakly coupled subsector of the latter can be treated within a perturbative setting, the strongly…

The zero momentum sectors in effective theories of QCD coupled to pseudoreal (two colors) and real (adjoint) quarks have alternative descriptions in terms of chiral orthogonal and symplectic ensembles of random matrices. Using this…

We derive the hole probability and the distribution of the smallest eigenvalue of chiral hermitian random matrices corresponding to Dirac operators coupled to massive quarks in QCD. They are expressed in terms of the QCD partition function…

The density operator is usually defined starting from a set of kets in the Hilbert space and a probability distribution. From this definition it is easy to obtain a factorization of a given density operator, here called density factor (DF).…

The relation between the spectral density of the QCD Dirac operator at nonzero baryon chemical potential and the chiral condensate is investigated. We use the analytical result for the eigenvalue density in the microscopic regime which…

We consider N=1, D=4 superconformal U(N)^{pq} Yang-Mills theories dual to AdS_5xS^5/Z_pxZ_q orbifolds. We construct the dilatation operator of this superconformal gauge theory at one-loop planar level. We demonstrate that a specific sector…

The low-lying spectrum of the Dirac operator is predicted to be universal, within three classes, depending on symmetry properties specified according to random matrix theory. The three universal classes are the orthogonal, unitary and…