Nonlocal regularisation of noncommutative field theories

We study noncommutative field theories, which are inherently nonlocal, using a Poincar\'e-invariant regularisation scheme which yields an effective, nonlocal theory for energies below a cut-off scale. After discussing the general features and the peculiar advantages of this regularisation scheme for theories defined in noncommutative spaces, we focus our attention onto the particular case when the noncommutativity parameter is inversely proportional to the square of the cut-off, via a dimensionless parameter $\eta$. We work out the perturbative corrections at one-loop order for a scalar theory with quartic interactions, where the signature of noncommutativity appears in $\eta$-dependent terms. The implications of this approach, which avoids the problems related to UV-IR mixing, are discussed from the perspective of the Wilson renormalisation program. Finally, we remark about the generality of the method, arguing that it may lead to phenomenologically relevant predictions, when applied to realistic field theories.Comment: 1+11 pages, 6 figures; v2: references added, typos corrected, conclusions unchange

Fuzzy Torus via q-Parafermion

We note that the recently introduced fuzzy torus can be regarded as a q-deformed parafermion. Based on this picture, classification of the Hermitian representations of the fuzzy torus is carried out. The result involves Fock-type representations and new finite dimensional representations for q being a root of unity as well as already known finite dimensional ones.Comment: 12pages, no figur

Tensor calculus on noncommutative spaces

It is well known that for a given Poisson structure one has infinitely many star products related through the Kontsevich gauge transformations. These gauge transformations have an infinite functional dimension (i.e., correspond to an infinite number of degrees of freedom per point of the base manifold). We show that on a symplectic manifold this freedom may be almost completely eliminated if one extends the star product to all tensor fields in a covariant way and impose some natural conditions on the tensor algebra. The remaining ambiguity either correspond to constant renormalizations to the symplectic structure, or to maps between classically equivalent field theory actions. We also discuss how one can introduce the Riemannian metric in this approach and the consequences of our results for noncommutative gravity theories.Comment: 17p; v2: extended version, to appear in CQ

Coexistence of spin canting and metamagnetism in a one-dimensional Mn(II) compound bridged by alternating double end-to-end and double end-on azido ligands and the analog co(II) compound

Metals in Catalysis, Biomimetics & Inorganic Material

Syntheses, spectroscopic and thermal analyses of the hofmann-type metal(II) tetra- cyanonickelate(II) pyridazine complexes: {[M(pdz)Ni(CN)4]∙H2O}n (M = Zn(II) or Cd(II))

Two new Hofmann-type complexes in the form of {[M(pdz)Ni(CN)4]·H2O}n [where pdz = pyridazine; M = Zn(II) and M = Cd(II)] have been synthesized as a powder and their structural properties have been characterized by vibrational (FT-IR and Raman) spectroscopy, thermal and elemental analysis. The spectral and thermal analysis results suggest that these complexes are similar in structure to the Hofmann type complexes and their structures consist of polymeric layers of │M−Ni(CN)4│∞ with the pdz bound to the metal (M) atom. DOI: http://dx.doi.org/10.4314/bcse.v29i3.

Syntheses and characterizations of the cyanide-bridged heteronuclear polymeric complexes with 2-ethylimidazole

Three new cyano-bridged heteronuclear polymeric complexes, [Cu(etim)3Ni(CN)4]n, {[Zn(etim)3Ni(CN)4]∙H2O}n and [Cd(etim)2Ni(CN)4]n (etim = 2-ethylimidazole, hereafter abbreviated as Cu–Ni–etim, Zn–Ni–etim and Cd–Ni–etim) have been prepared in powder form and characterized by FT-IR and Raman spectroscopies, thermal (TG, DTG and DTA) and elemental analyses. The spectral features of the complexes suggest that the Ni(II) ion is four coordinate with four cyanide-carbon atoms in a square planar geometry, whereas the Cu(II) and the Zn(II) ions of the Cu–Ni–etim and the Zn–Ni–etim complexes are completed by nitrogen atoms of two cyano groups of [Ni(CN)4]2- coordinated to the adjacent M(II) ions and three nitrogen atoms of the etim ligands. The Cd(II) ion of the Cd–Ni–etim complex is six-coordinate, completed with the two nitrogen atoms of the etim ligands and the four nitrogen atoms from bridging cyano groups. Polymeric structures of the Cu–Ni–etim and the Zn–Ni–etim complexes are 1D coordination polymer, while complex the Cd–Ni–etim presents a 2D network. The thermal decompositions in the temperature range 30–700 °C of the complexes were investigated in the static air atmosphere

Chaotic Dynamics of the Mass Deformed ABJM Model

We explore the chaotic dynamics of the mass deformed ABJM model. To do so, we first perform a dimensional reduction of this model from $2+1$- to $0+1$-dimensions, considering that the fields are spatially uniform. Working in the 't Hooft limit and tracing over ansatz configurations involving fuzzy two spheres, which are described in terms of the GRVV matrices with collective time dependence, we obtain a family of reduced effective Lagrangians and demonstrate that they have chaotic dynamics by computing the associated Lyapunov spectrum. In particular, we analyze in detail, how the largest Lyapunov exponent, $\lambda_L$, changes as a function of $E/N^2$. Depending on the structure of the effective potentials, we find either $\lambda_L \propto (E/N^2)^{1/3}$ or $\lambda_L \propto (E/N^2 - \gamma_N)^{1/3}$, where $\gamma_N(k, \mu)$ is a constant determined in terms of the Chern-Simons coupling $k$, the mass $\mu$, and the matrix level $N$. Using our results, we investigate the temperature dependence of the largest Lyapunov exponents and give upper bounds on the temperature above which $\lambda_L$ values comply with the MSS bound, $\lambda_L \leq 2 \pi T$, and below which it will eventually be violated.Comment: 35 pages, 8 figure

Chaos from equivariant fields on fuzzy S 4

Abstract We examine the 5d Yang-Mills matrix model in 0 + 1-dimensions with U(4N) gauge symmetry and a mass deformation term. We determine the explicit SU(4) ≈ SO(6) equivariant parametrizations of the gauge field and the fluctuations about the classical four concentric fuzzy four sphere configuration and obtain the low energy reduced actions(LEAs) by tracing over the S F 4 s for the first five lowest matrix levels. The LEAs so obtained have potentials bounded from below indicating that the equivariant fluctuations about the S F 4 do not lead to any instabilities. These reduced systems exhibit chaos, which we reveal by computing their Lyapunov exponents. Using our numerical results, we explore various aspects of chaotic dynamics emerging from the LEAs. In particular, we model how the largest Lyapunov exponents change as a function of the energy. We also show that, in the Euclidean signature, the LEAs support the usual kink type soliton solutions, i.e. instantons in 1+ 0-dimensions, which may be seen as the imprints of the topological fluxes penetrating the concentric S F 4 s due to the equivariance conditions, and preventing them to shrink to zero radius. Relaxing the Gauss law constraint in the LEAs in the manner recently discussed by Maldacena and Milekhin leads to Goldstone bosons