Noncommutative Model Research Articles

Quantum aspects of the noncommutative Sine-Gordon model

In this paper, we first use semi-classical methods to study quantum field theoretical aspects of the integrable noncommutative sine-Gordon model proposed in [hep-th/0406065]. In particular, we examine the fluctuations at quadratic order around the static kink solution using the background field method. We derive equations of motion for the fluctuations and argue that at O(θ2) the spectrum of fluctuations remains essentially the same as that of the corresponding commutative theory. We compute the one-loop two-point functions of the sine-Gordon field and the additional scalar field present in the model and exhibit logarithmic divergences, only some of which lead to UV/IR mixing. We briefly discuss the one-loop renormalization in Euclidean signature and comment on the obstacles in determining the noncommutativity corrections to the quantum mass of the kink.

Slow-roll reconstruction for running spectral index

We reconstruct from the Wilkinson microwave anisotropy probe three-year data the slow-roll parameters in the standard slow-roll inflation model and the noncommutative inflation model. We also investigate the evolution of these slow-roll parameters. Requiring that slow-roll inflation lasts more than 20 e-folds after cosmic microwave background scales leave the horizon, we find that the potential at the last stage of inflation takes the form $V(\ensuremath{\phi})={V}_{0}(1+\frac{{\ensuremath{\eta}}_{c}}{2}\frac{(\ensuremath{\phi}\ensuremath{-}{\ensuremath{\phi}}_{c}{)}^{2}}{{M}_{p}^{2}})$, where ${\ensuremath{\eta}}_{c}$ is a constant. A natural mechanism to end inflation at $\ensuremath{\phi}={\ensuremath{\phi}}_{c}$ is the hybrid-type inflation.

Renormalization of the Orientable Non-commutative Gross–Neveu Model

We prove that the non-commutative Gross-Neveu model on the two-dimensional Moyal plane is renormalizable to all orders. Despite a remaining UV/IR mixing, renormalizability can be achieved. However, in the massive case, this forces us to introduce an additional counterterm of the form psibar i gamma^{0} gamma^{1} psi. The massless case is renormalizable without such an addition.

Ginsparg-Wilson Relation and Admissibility Condition in Noncommutative Geometry

Ginsparg-Wilson relation and admissibility condition have the key role to construct lattice chiral gauge theories. They are also useful to define the chiral structure in finite noncommutative geometries or matrix models. We discuss their usefulness briefly.

Propagators for Noncommutative Field Theories

In this paper we provide exact expressions for propagators of noncommutative Bosonic or Fermionic field theories after adding terms of the Grosse-Wulkenhaar type to the usual free action in order to ensure Langmann–Szabo covariance. We emphasize the new Fermionic case and we give in particular all necessary bounds for the multiscale analysis and renormalization of the noncommutative Gross-Neveu model.

Running of the running of the spectral index and WMAP three-year data

The three-year WMAP (Wilkinson microwave anisotropy probe) data imply not only anegative running of the spectral index with large absolute value, but also a largepositive running of the running of the spectral index with the order of magnitude10−2. We calculate the running of the running in the usual inflation modeland the non-commutative inflation model. A large tensor–scalar ratior≥1.23 is needed in order to fit the WMAP data in the non-commutative inflation model, whichroughly saturates the observational upper bound on it.

Photon Defects in Noncommutative Standard Model Candidates

Restrictions imposed by gauge invariance in noncommutative spaces together with the effects of ultraviolet/infrared mixing lead to strong constraints on possible candidates for a noncommutative extension of the Standard Model. We study a general class of noncommutative models consistent with these restrictions. Specifically we consider models based upon a gauge theory with the gauge group U(N1) × U(N2) × ... × U(Nm) coupled to matter fields transforming in the (anti)-fundamental, bi-fundamental and adjoint representations. We pay particular attention to overall trace-U(l) factors of the gauge group which are affected by the ultraviolet/infrared mixing. Typically, these trace-U(l) gauge fields do not decouple sufficiently fast in the infrared, and lead to sizable Lorentz symmetry violating effects in the low-energy effective theory. In a 4-dimensional theory on a continuous space-time making these effects unobservable would require making the effects of noncommutativity tiny, MNC >> Mp. This severely limits the phenomenological prospects of such models. However, adding additional universal extra dimensions the trace-U(l) factors decouple with a power law and the constraint on the noncommutativity scale is weakened considerably. Finally, we briefly mention some interesting properties of the photon that could arise if the noncommutative theory is modified at a high energy scale.

Running spectral index in noncommutative inflation and WMAP three year results

A model independent analysis shows that the running of the spectral index of the three year WMAP results can be nicely realized in noncommutative inflation. We also re-examine some concrete noncommutative inflation models. We find that a large tensor–scalar ratio is required, corresponding to a low number of e-folds before the end of inflation in some simple models.

Vortices in U(1) noncommutative gauge fields

Charged vortex solutions for noncommutative Maxwell-Higgs model in 3+1 dimensions are found. We show that the stability of these vortex solutions is spoiled out for some, large enough, noncommutativity parameter. A non topological charge, however, is induced by noncommutative effects.

Noncommutative chaotic inflation and WMAP three year results

Abstract Noncommutative inflation is based upon the consideration of some effects of the space–time uncertainty principle motivated by ideas from string/M theory. The CMB anisotropies may carry a signature of this very early Universe correction from the space–time uncertainty principle and can be used to place constraints on the parameters of the noncommutative inflation model. In this Letter we analyze the noncommutative chaotic inflation model by means of the WMAP three year results. We show that the noncommutative chaotic inflation model can produce a large negative running of spectral index within a reasonable range of e-folding number N, provided that the value of p in the potential V ( ϕ ) ∝ ϕ p is enhanced roughly to p ∼ 12 – 18 . Applying a likelihood analysis to the WMAP results, we find the best-fit values of parameters for the noncommutative chaotic inflation model. In addition, this model predicts a rather big gravitational wave which may be tested by the upcoming experiments.

Noncommutative 6D gauge Higgs unification models

The influence of higher dimensions in noncommutative field theories is considered. For this purpose, we analyze the bosonic sector of a recently proposed 6 dimensional SU(3) orbifold model for the electroweak interactions. The corresponding noncommutative theory is constructed by means of the Seiberg-Witten map in 6D. We find in the reduced bosonic interactions in 4D theory, couplings which are new with respect to other known 4D noncommutative formulations of the Standard Model using the Seiberg-Witten map. Phenomenological implications due to the noncommutativity of extra dimensions are explored. In particular, assuming that the commutative model leads to the standard model values, a bound -5.63 10^{-8} GeV^{-2}< theta <1.06 10^{-7}GeV^{-2} on the corresponding noncommutativity scale is derived from current experimental constraints on the S and T oblique parameters. This bound is used to predict a possibly significant impact of noncommutativity effects of extra dimensions on the rare Higgs boson decay H-> gamma gamma.

About the self-dual Chern–Simons system and Toda field theories on the noncommutative plane

The relation of the noncommutative self-dual Chern–Simons (NCSDCS) system to the noncommutative generalizations of Toda and of affine Toda field theories is investigated more deeply. This paper continues the programme initiated in (Cabrera-Carnero I 2005 J. High Energy Phys. JHEP10(2005)071), where it was presented how it is possible to define Toda field theories through second order differential equation systems starting from the NCSDCS system. Here we show that using the connection of the NCSDCS to the noncommutative chiral model, exact solutions of the Toda field theories can also be constructed by means of the noncommutative extension of the uniton method proposed in (Lee K-M 2004 J. High Energy Phys. JHEP08(2004)054) by Lee. Particularly some specific solutions of the nc Liouville model are explicitly constructed.

Spontaneous reduction of noncommutative gauge symmetry and model building

We propose a mechanism for the spontaneous (gauge-invariant) reduction of noncommutative ${\cal U}(n)$ gauge theories down to SU(n). This can be achieved through the condensation of composite ${\cal U}(n)$ gauge invariant fields that involves half-infinite Wilson lines in trace-U(1) noninvariant and SU(n) preserving direction. Based on this mechanism we discuss anomaly-free fully gauge invariant noncommutative Standard Model based on the minimal gauge group ${\cal U}(3)\times {\cal U}(2)\times {\cal U}(1)$, previously proposed, and show how it can be consistently reduced to the Standard Model with the usual particle spectrum. Charge quantization for quarks and leptons naturally follows from the model.

Lorentz symmetry breaking in the noncommutative Wess-Zumino model: One loop corrections

In this paper we deal with the issue of Lorentz symmetry breaking in quantum field theories formulated in a non-commutative space-time. We show that, unlike in some recente analysis of quantum gravity effects, supersymmetry does not protect the theory from the large Lorentz violating effects arising from the loop corrections. We take advantage of the non-commutative Wess-Zumino model to illustrate this point.

Telltale traces of U(1) fields in noncommutative standard model extensions

Restrictions imposed by gauge invariance in noncommutative spaces together with the effects of ultraviolet/infrared mixing lead to strong constraints on possible candidates for a noncommutative extension of the Standard Model. In this paper, we study a general class of 4-dimensional noncommutative models consistent with these restrictions. Specifically we consider models based upon a gauge theory with the gauge group U(N_1)\times U(N_2) \times ... \times U(N_m) coupled to matter fields transforming in the (anti)-fundamental, bi-fundamental and adjoint representations. Noncommutativity is introduced using the Weyl-Moyal star-product approach on a continuous space-time. We pay particular attention to overall trace-U(1) factors of the gauge group which are affected by the ultraviolet/infrared mixing. We show that, in general, these trace-U(1) gauge fields do not decouple sufficiently fast in the infrared, and lead to sizable Lorentz symmetry violating effects in the low-energy effective theory. Making these effects unobservable in the class of models we consider would require pushing the constraint on the noncommutativity mass scale far beyond the Planck mass (M_{NC}\gtrsim 10^{100} M_{P}) and severely limits the phenomenological prospects of such models.

Noncommutative two-dimensional BF model

We consider the noncommutative extension of the BF theory in two spacetime dimensions. We show that the introduction of the noncommutative parameter θµν , already at first order in the analytical sector, induces infinitely many terms in the quantum extension of the model. This clashes with the commonly accepted rules of QFT, and we believe that this problem is not peculiar to this particular model, but it might concern the noncommutative extension of any ordinary quantum field theory obtained via the Moyal prescription. A detailed study of noncommutative anomalies is also presented.

Non-commutative multi-dimensional cosmology

A non-commutative multi-dimensional cosmological model is introduced and used to address the issues of compactification and stabilization of extra dimensions and the cosmological constant problem. We show that in such a scenario these problems find natural solutions in a universe described by an increasing time parameter.

Spontaneous reduction of noncommutative gauge symmetry and model building

Spontaneous reduction of noncommutative gauge symmetry and model building

Noncommutative space-time models

The FRT quantum Euclidean spaces O N q are formulated in terms of Cartesian generators. The quantum analogs of N-dimensional Cayley-Klein spaces are obtained by contractions and analytical continuations. Noncommutative constant-curvature spaces are introduced as spheres in the quantum Cayley-Klein spaces. For N = 5 part of them is interpreted as the noncommutative analogs of (1+3) space-time models. As a result the quantum (anti) de Sitter, Minkowski, Newton, Galilei kinematics with the fundamental length and the fundamental time are suggested.

Conserved quantities in the noncommutative principal chiral model with Wess–Zumino term

We construct noncommutative extension of U(N) principal chiral model with Wess-Zumino term and obtain an infinite set of local and non-local conserved quantities for the model using iterative procedure of Brezin {\it et.al} \cite{BIZZ}. We also present the equivalent description as Lax formalism of the model. We expand the fields perturbatively and derive zeroth- and first-order equations of motion, zero-curvature condition, iteration method, Lax formalism, local and non-local conserved quantities.