Related papers: Supersymmetric QCD in the Noncommutative Geometry
In this paper, we present the quadratic associative symmetry algebra of the 3D nondegenerate maximally quantum superintegrable system. This is the complete symmetry algebra of the system. It is demonstrated that the symmetry algebra…
A review of the construction of a Weyl-invariant spinning-membrane action that is $polynomial$ in the fields, without a cosmological constant term, comprised of quadratic and quartic-derivative terms, and where supersymmetry is linearly…
A review of the applications of noncommutative geometry to a systematic formulation of duality symmetries in string theory is presented. The spectral triples associated with a lattice vertex operator algebra and the corresponding…
We study four dimensional supersymmetric gauge theory on the noncommutative superspace, recently proposed by Seiberg. We construct the gauge-invariant action of N=1 super Yang-Mills theory with chiral and antichiral superfields, which has…
Chiral symmetry provides the symmetry protection for a large class of topological edge states. It exists in non-Hermitian systems as well, and the same anti-commutation relation between the Hamiltonian and a linear chiral operator, i.e.,…
This PhD thesis aims at combining the framework of noncommutative geometry and supersymmetry. A particular class of non-commutative geometries called almost-commutative geometries can be used to describe particle theories. This thesis…
In the last few years, the supersymmetry method was generalized to real-symmetric, Hermitean, and Hermitean self-dual random matrices drawn from ensembles invariant under the orthogonal, unitary, and unitary symplectic group, respectively.…
Some years ago, one of the authors~(MM) revived a concept to which he gave the name of single-particle Dirac oscillator, while another~(CQ) showed that it corresponds to a realization of supersymmetric quantum mechanics. The Dirac…
In this paper we use considerations of non-commutative geometry to deduce a model for QCD interactions. The model also explains within the same theoretical framework hitherto purely phenomenological characteristics of the quarks like their…
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…
Dynamical chiral symmetry breaking is a nonperturbative phenomenon that may be studied using QCD's gap equation. Model-independent results can be obtained with a nonperturbative and symmetry preserving truncation. The gap equation yields…
We present all NSR superstring and super-D-string actions invariant under a set of prescribed gauge transformations, and characterize completely their global symmetries. In particular we obtain locally supersymmetric Born-Infeld actions on…
We re-examine the non Hermitian position coordinate of Dirac's equation, in the light of his own insights and conclude that this, and the Dirac equation itself is symptomatic of an underlying Noncommutative Geometry.
In this chapter of the Oxford Handbook of Random Matrix Theory we introduce chiral Random Matrix Theories with the global symmetries of QCD. In the microscopic domain, these theories reproduce the mass and chemical potential dependence of…
The most general Dirac Hamiltonians in $(1+1)$ dimensions are revisited under the requirement to exhibit a supersymmetric structure. It is found that supersymmetry allows either for a scalar or a pseudo-scalar potential. Their spectral…
Integration of the Dirac equation with an external electromagnetic field is explored in the framework of the method of separation of variables and of the method of noncommutative integration. We have found a new type of solutions that are…
Consider a formally self-adjoint first order linear differential operator acting on pairs (2-columns) of complex-valued scalar fields over a 4-manifold without boundary. We examine the geometric content of such an operator and show that it…
The paper considers a Clifford extension of the Grassmann algebra, in which operators are built from Grassmann variables and by the derivatives with respect to them. It is shown that a subalgebra which is isomorphic to the usual matrix…
We present examples of equivariant noncommutative Lorentzian spectral geometries. The equivariance with respect to a compact isometry group (or quantum group) allows to construct the algebraic data of a version of spectral triple geometry…
A few years ago, we found the supersymmetric(SUSY) counterpart of the spectral triple which specified noncommutative geometry(NCG). Based on "the triple", we considered the SUSY version of the spectral action principle and had derived the…