Noncommutative Scale Research Articles

Noncommutative radial waves

We study radial waves in a (2+1)-dimensional noncommutative scalar field theory, using operatorial methods. The waves propagate along a discrete radial coordinate and are described by finite series deformations of Bessel-type functions. At radius much larger than the noncommutativity scale , one recovers the usual commutative behaviour. At small distances, classical divergences are smoothed out by noncommutativity.

Green-Schwarz superstring from type IIB matrix model

We construct a Green-Schwarz (GS) light-cone closed superstring theory from the type IIB matrix model. A GS light-cone string action is derived from the two-dimensional $\mathcal{N}=8\text{ }\text{ }U(n)$ noncommutative Yang-Mills (NCYM) theory by identifying a noncommutative scale with a string scale. The supersymmetry transformation for the light-cone gauge action is also derived from supersymmetry transformation for the IIB matrix model. By identifying the physical states and interaction vertices, string theory is perturbatively reproduced.

Noncommutative real scalar field theory in 2+1 dimensions at finite temperature

We study thermal effects for a noncommutative real scalar field in 2+1 dimensions including a Grosse-Wulkenhaar term. Using a perturbative expansion for the free energy, we deduce some general properties of the corresponding contributions, in the thermodynamic limit. We show that the model can be consistently interpreted as defined on a finite volume, which is naturally determined by the noncommutativity scale.

Casimir effect in [formula omitted]-dimensional noncommutative theories

We study the Dirichlet Casimir effect for a complex scalar field on two noncommutative spatial coordinates plus a commutative time. To that end, we introduce Dirichlet-like boundary conditions on a curve contained in the spatial plane, in such a way that the correct commutative limit can be reached. We evaluate the resulting Casimir energy for two different curves: (a) Two parallel lines separated by a distance L, and (b) a circle of radius R. In the first case, the resulting Casimir energy agrees exactly with the one corresponding to the commutative case, regardless of the values of L and of the noncommutativity scale θ, while for the latter the commutative behaviour is only recovered when R≫θ. Outside of that regime, the dependence of the energy with R is substantially changed due to noncommutative corrections, becoming regular for R→0.

A non-commutative version of the minimal supersymmetric standard model

A minimal supersymmetric standard model on non-commutative space-time (NC MSSM) is proposed. The model fulfills the requirements of non-commutative gauge invariance and the absence of anomaly. The existence of supersymmetry with a scale of its breaking lower than the non-commutative scale is crucial in order to achieve consistent gauge symmetry breaking.

Noncommutative Bianchi Type II Quantum Cosmology

In this paper we present the noncommutative Bianchi Class A cosmological models coupled to barotropic perfect fluid. The commutative and noncommutative quantum solution to the Wheeler–DeWitt equation for any factor ordering, to the anisotropic Bianchi type II cosmological model are found, using a stiff fluid (γ=1). In our toy model, we introduce noncommutative scale factors, is say, we consider that all minisuperspace variables qi does not commute, so the simplectic structure was modified.

Graviton propagators in supergravity and noncommutative gauge theory

We investigate the graviton propagator in the type IIB supergravity background which is dual to 4 dimensional noncommutative gauge theory. We assume that the boundary is located not at the infinity but at the noncommutative scale where the string frame metric exhibits the maximum. We argue that the Neumann boundary condition is the appropriate boundary condition to be adopted at the boundary. We find that the graviton propagator behaves just as that of the 4 dimensional massless graviton. On the other hand, the non-analytic behaviors of the other Kaluza-Klein modes are not significantly affected by the Neumann boundary condition.

T-duality with H-flux: Non-commutativity, T-folds and [formula omitted] structure

Various approaches to T-duality with NSNS three-form flux are reconciled. Non-commutative torus fibrations are shown to be the open-string version of T-folds. The non-geometric T-dual of a three-torus with uniform flux is embedded into a generalized complex six-torus, and the non-geometry is probed by D0-branes regarded as generalized complex submanifolds. The non-commutativity scale, which is present in these compactifications, is given by a holomorphic Poisson bivector that also encodes the variation of the dimension of the world-volume of D-branes under monodromy. This bivector is shown to exist in SU ( 3 ) × SU ( 3 ) structure compactifications, which have been proposed as mirrors to NSNS-flux backgrounds. The two SU ( 3 ) -invariant spinors are generically not parallel, thereby giving rise to a non-trivial Poisson bivector. Furthermore we show that for non-geometric T-duals, the Poisson bivector may not be decomposable into the tensor product of vectors.

Light propagation in a background field for time–space non-commutativity and axionic non-commutative QED

We study the low-energy effects of space–time non-commutativity on light propagation in a background electromagnetic field. Contrary to some of the previous claims, we find no polarization rotation for vanishing time–space commutator [ x ˆ i , x ˆ 0 ] = 0 , although dispersion relation is modified, allowing for propagation faster than the vacuum speed of light. For non-zero [ x ˆ i , x ˆ 0 ] , as allowed with a proper quantization, a naive rotation effect is found to be actually absent when physical fields are defined through Seiberg–Witten map. We also consider non-commutative QED weakly coupled to small mass particles such as axions. Non-commutativity is found to dominate the inverse oscillation length, compared to axion mass and QED effects, for mixing particle masses smaller than 10 −12 eV . Conventional constraints on axion coupling based on photon–axion transition rates are unmodified, however induced ellipticity is proportional to the non-commutativity squared length scale. This last effect is found to be too small to account for the ellipticity reported by the PVLAS experiment, yet unexplained by conventional QED or axion physics.

Tunneling between de Sitter and anti-de Sitter black holes in a noncommutativeD3-brane formalism

We obtain de Sitter (dS) and anti-de Sitter (AdS) generalized Reissner-Nordstrom\char21{}like black hole geometries in a curved ${\mathrm{D}}_{3}$-brane framework, underlying a noncommutative gauge theory on the brane world. The noncommutative scaling limit is explored to investigate a possible tunneling of an AdS vacuum in string theory to dS vacuum in its low energy gravity theory. The Hagedorn transition is invoked into its self-dual gauge theory to decouple the gauge nonlinearity from the dS geometry, which in turn is shown to describe a pure dS vacuum.

Weak gravity conjecture for noncommutative field theory

We investigate the weak gravity bounds on the U(1) gauge theory and scalar field theories in various dimensional noncommutative space. Many results are obtained, such as the upper bound on the noncommutative scale $g_{YM}M_p$ for four dimensional noncommutative U(1) gauge theory. We also discuss the weak gravity bounds on their commutative counterparts. For example, our result on 4 dimensional noncommutative U(1) gauge theory reduces in certain limit to its commutative counterpart suggested by Arkani-Hamed et.al at least at tree-level.

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.

Noncommutative brane-world, (Anti) de Sitter vacua and extra dimensions

We investigate a curved brane-world, inspired by a noncommutative D3-brane, in a type IIB string theory. We obtain, an axially symmetric and a spherically symmetric, (anti) de Sitter black holes in 4D. The event horizons of these black holes possess a constant curvature and may be seen to be governed by different topologies. The extremal geometries are explored, using the noncommutative scaling in the theory, to reassure the attractor behavior at the black hole event horizon. The emerging two dimensional, semi-classical, black hole is analyzed to provide evidence for the extra dimensions in a curved brane-world. It is argued that the gauge nonlinearity in the theory may be redefined by a potential in a moduli space. As a result, D=11 and D=12 dimensional geometries may be obtained at the stable extrema of the potential.

Vacuum birefringence as a probe of Planck scale noncommutativity

Because of ultraviolet/infrared (UV/IR) mixing, the low energy physics of noncommutative gauge theories in the Moyal-Weyl approach seems to depend crucially on the details of the ultraviolet completion. However, motivated by recent string theory analyses, we argue that their phenomenology with a very general class of UV completions can be accurately modelled by a cutoff close to the Planck scale. In the infrared the theory tends continuously to the commutative gauge theory. If the photon contains contributions from a trace-U(1), we would observe vacuum birefringence, i.e. a polarisation dependent propagation speed, as a residual effect of the noncommutativity. Constraints on this effect require the noncommutativity scale to be close to the Planck scale.

Noncommutative Kachru-Kallosh-Linde-Maldacena-McAllister-Trivedi model

In the noncommutative spacetime the fine tuning in KKLMMT model can be significantly released and a nice running of spectral index fitting the WMAP 3 yr data can be achieved. The fitting results show that the noncommutative mass scale is roughly $5\ifmmode\times\else\texttimes\fi{}{10}^{14}\text{ }\text{ }\mathrm{Gev}$. The string mass scale is higher than the noncommutative scale unless the string coupling is smaller than ${10}^{\ensuremath{-}10}$.

Quantum mechanics on noncommutative spacetime

We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a nonrelativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical noncommutative spacetime. An interesting new feature of quantum mechanics formulated on a noncommutative spacetime is an intrinsic electric dipole moment. We note, however, that noncommutative intrinsic dipole moments are not observable in present experiments searching for an electric dipole moment of leptons or nuclei such as the neutron since they are spin independent. These experiments are sensitive to the energy difference between two states and the noncommutative effect thus cancels out. Bounds on the noncommutative scale found in the literature relying on such intrinsic electric dipole moments are thus incorrect.

Semileptonic decay of a polarized top quark in the noncommutative standard model

In this paper we study the noncommutative effects to the lepton spectrum from the decay of a polarized top quark. It is shown that the lowest contribution comes from the quadratic terms of the noncommutative parameter. The deviations from the standard model are significant for small values of the noncommutative characteristic scale. However, the charged lepton spin correlation coefficient has a remarkable deviation from the standard model from very low values of the noncommutative characteristic scale to 1 TeV.

Probe noncommutative space–time scale using γγ→Z at ILC

In the standard model production of on-shell Z boson at a photon collider (or Z decays into $\gamma\gamma$) is strictly forbidden by angular momentum conservation and Bose statistics (the Yang's Theorem). In the standard model with noncommutative space-time this process can occur. Therefore this process provides an important probe for the noncommutative space-time. The $\gamma\gamma$ collision at the ILC by laser backscattering of the electron and positron beams offers an ideal place to carry out such a study. Assuming an integrated luminosity of 500 fb$^{-1}$, we show that the constraint which can be achieved on $\Gamma(Z\to \gamma \gamma)$ is three to four orders of magnitude better than the current bound of $5.2\times 10^{-5}$ GeV. The noncommutative scale can be probed up to a few TeVs.

Unusual high-energy phenomenology of Lorentz-invariant noncommutative field theories

It has been suggested that one may construct a Lorentz-invariant noncommutative field theory by extending the coordinate algebra to additional, fictitious coordinates that transform nontrivially under the Lorentz group. Integration over these coordinates in the action produces a four-dimensional effective theory with Lorentz invariance intact. Previous applications of this approach, in particular to a specific construction of noncommutative QED, have been studied only in a low-momentum approximation. Here we discuss Lorentz-invariant field theories in which the relevant physics can be studied without requiring an expansion in the inverse scale of noncommutativity. Qualitatively, we find that tree-level scattering cross sections are dramatically suppressed as the center-of-mass energy exceeds the scale of noncommutativity, that cross sections that are isotropic in the commutative limit can develop a pronounced angular dependence, and that nonrelativistic potentials (for example, the Coloumb potential) become nonsingular at the origin. We consider a number of processes in noncommutative QED that may be studied at a future linear collider. We also give an example of scattering via a four-fermion operator in which the noncommutative modifications of the interaction can unitarize the tree-level amplitude, without requiring any other new physics in the ultraviolet.

Holography and D3-branes in Melvin universes

Recently, Hashimoto and Thomas [J. High Energy Phys., 01 (2006) 083] found that noncommutative super Yang-Mills (NCSYM) theory with space-dependent noncommutativity can be formulated as a decoupling limit of open strings ending on D3-branes wrapping a Melvin universe supported by a flux of the NSNS B-field. Under S-duality, we show that this theory turns into a noncommutative open string (NCOS) theory with space-dependent space-time noncommutativity and effective space-dependent string scale. It is an NCOS theory with both space-dependent space-space and space-time noncommutativities under more general SL(2,Z) transformation. These space-dependent noncommutative theories (NCSYM and NCOS) have completely the same thermodynamics as that of ordinary super YM theory, NCSYM and NCOS theories with constant noncommutativity in the dual supergravity description. Starting from black D3-brane solution in the Melvin universe and making a Lorentz boost along one of spatial directions on the worldvolume of D3-branes, we show that the decoupled theory is a lightlike NCSYM theory with space-dependent noncommutativity in a static frame or in an infinite-momentum frame depending on whether there is a gravitational pp-wave on the worldvolume of the D3-branes.