Related papers: Supersymmetric QCD in the Noncommutative Geometry
We review a procedure of factorizing the Minkowski space Dirac operator over a~suitable superspace, discuss its Euclidean space version and apply the worked out formalism in the case od an almost-commutative Dirac operator. The presented…
Within a four dimensional N = 1 superspace, we present a new ansatz for the Skyrme term and for the gauged WZNW term embedded into a superaction. We use the new chiral-nonminimal (CNM) formulation for the effective low-energy action of 4D,…
The aim of this paper is to present a possible framework for incorporating a superspace formulation of supersymmetry into the formalism of noncommutative geometry \`a la Alain Connes. In analogy with the almost-commutative (AC) manifold…
In the presence of a non-vanishing chemical potential the eigenvalues of the Dirac operator become complex. We calculate spectral correlation functions of complex eigenvalues using a random matrix model approach. Our results apply to…
I will summarize Noncommutative Geometry Spectral Action, an elegant geometrical model valid at unification scale, which offers a purely gravitational explanation of the Standard Model, the most successful phenomenological model of particle…
We propose a symmetry of the Dirac equation under the interchange of signs of eigenvalues of the Dirac's $K$ operator. We show that the only potential which obeys this requirement is the Coulomb one for both vector and scalar cases.…
We briefly review the overlap formalism for chiral gauge theories, the overlap Dirac operator for massless fermions and its connection to domain wall fermions. We describe properties of the overlap Dirac operator, and methods to implement…
It is shown that the main geometrical objects involved in all the symmetries or supersymmetries of the Dirac operators in curved manifolds of arbitrary dimensions are the Killing vectors and the Killing-Yano tensors of any ranks. The…
We construct a metric structure on a configuration space of gauge connections and show that it naturally produces a candidate for a non-perturbative, 3+1 dimensional Yang-Mills-Dirac quantum field theory on a curved background. The metric…
In this paper, we derive the five-dimensional non-Abelian $\mathcal{N}=1$ Chern-Simons action from its established definition of variation with respect to an infinitesimal deformation of the vector prepotential in a projective superspace…
Quiver varieties have recently appeared in various different areas of Mathematics such as representation theory of Kac-Moody algebras and quantum groups, instantons on 4-manifolds, and resolutions Kleinian singularities. In this paper, we…
The aim of the present paper is to introduce the notion of first order (supersymmetric) Dirac operators on discrete and metric (``quantum'') graphs. In order to cover all self-adjoint boundary conditions for the associated metric graph…
We present a closed-form expression for the supersymmetric non-Abelian Chern-Simons action in conventional five-dimensional N=1 superspace. Our construction makes use of the superform formalism to generate supersymmetric invariants. Similar…
We investigate the notion of subsystem in the framework of spectral triple as a generalized notion of noncommutative submanifold. In the case of manifolds, we consider several conditions on Dirac operators which turn embedded submanifolds…
In the preceding paper [arXiv:hep-th/0604217], we construct the Dirac operator and the integral on the canonical noncommutative space. As a matter of fact, they are ones on the noncommutative torus. In the present article, we introduce the…
In the past ten years, the ideas of supersymmetry have been profitably applied to many nonrelativistic quantum mechanical problems. In particular, there is now a much deeper understanding of why certain potentials are analytically solvable…
Quark spectra in QCD are linked to fundamental properties of the theory including the identification of pions as the Goldstone bosons of spontaneously broken chiral symmetry. The lattice Overlap-Dirac operator provides a nonperturbative,…
A finite non-commutative geometry consists of a fuzzy space together with a Dirac operator satisfying the axioms of a real spectral triple. This paper addreses the question of how to extract information about these geometries from the…
Noncommutative geometry has seen remarkable applications for high energy physics, viz. the geometrical interpretation of the Standard Model. The question whether it also allows for supersymmetric theories has so far not been answered in a…
We reinvestigate constraints on the eigenvalue density of the Dirac operator in the chiral symmetric phase of 2 flavor QCD at finite temperature, employing the overlap Dirac operator with the exact chiral symmetry at finite lattice spacings…