We consider an interacting scalar quantum field theory on noncommutative Euclidean space. We implement a family of noncommutative deformations, which -- in contrast to the well known Moyal-Weyl deformation -- lead to a theory with modified kinetic term, while all local potentials are unaffected by the deformation. We show that our models, in particular, include propagators with anisotropic scaling z=2 in the ultraviolet (UV). For a Φ^4-theory on our noncommutative space we obtain an improved UV behaviour at the one-loop level and the absence of UV/IR-mixing and of the Landau pole.
We consider quantum electrodynamics in noncommutative spacetime by deriving a $θ$-exact Seiberg-Witten map with fermions in the fundamental representation of the gauge group as an expansion in the coupling constant. Accordingly, we demonstrate the persistence of UV/IR mixing in noncommutative QED with charged fermions via Seiberg-Witten map, extending the results of Schupp and You [1].
There have been comments on the starting paper, hep-th/0106074, which point out unclear motivation and definitions on noncommutative momentum introduced. This paper is withdrawn by the author for more clear presentation.
Noncommutative gauge theories defined via Seiberg-Witten map have desirable properties that theories defined directly in terms of noncommutative fields lack, covariance and unrestricted choice of gauge group and charge being among them, but nonperturbative results in the deformation parameter θare hard to obtain. In this article we use a θ-exact approach to study UV/IR mixing in a noncommutative quantum electrodynamics (NCQED) model defined via Seiberg-Witten map. The fermion contribution of the one loop correction to the photon propagator is computed and it is found that it gives the same UV/…
In this letter we will dicuss the possibility of a resummation procedure in order to cure the UV/IR-mixing problem of noncommutative field theories. The method is presented for a scalar phi^4 theory on Euclidean space. Finally, we sketch the idea of resummation for U(1)-gauge theories.
The IR/UV mixing and the violation of unitarity are two of the most intriguing aspects of noncommutative quantum field theories. In this paper the relation between these two phenomena is explained and established. We start out by showing that the S-matrix of noncommutative field theories is hermitian analytic. As a consequence, a noncommutative field theory is unitary if the discontinuities of its Feynman diagram amplitudes agree with the expressions calculated using the Cutkosky formulae. These unitarity constraints relate the discontinuities of amplitudes with physical intermediate states; a…
We show that there are one-loop IR singularities arising from UV/IR mixing in noncommutative SU(N) Yang-Mills theory defined by means of the $θ$-exact Seiberg-Witten map. This is in spite of the fact that there are no ordinary U(1) gauge fields in the theory and this is at variance with the noncommutative U(N) case, where the two-point part of the effective action involving the ordinary SU(N) fields do not suffer from those one-loop IR singularities.
Using path integral method (Fujikawa's method) we calculate anomalies in noncommutative gauge theories with fermions in the bi-fundamental and adjoint representations. We find that axial and chiral gauge anomalies coming from non-planar contributions are derived in the low noncommutative momentum limit $\widetilde{p}^μ(\equiv θ^{μν}p_ν) \to 0$. The adjoint chiral fermion carries no anomaly in the non-planar sector in $D=4k (k=1,2,...,)$ dimensions. It is naturally shown from the path integral method that anomalies in non-planar sector originate in UV/IR mixing.
Scalar field theories with quartic interaction are quantized on fuzzy $S^2$ and fuzzy $S^2\times S^2$ to obtain the 2- and 4-point correlation functions at one-loop. Different continuum limits of these noncommutative matrix spheres are then taken to recover the quantum noncommutative field theories on the noncommutative planes ${\mathbb R}^2$ and ${\mathbb R}^4$ respectively. The canonical limit of large stereographic projection leads to the usual theory on the noncommutative plane with the well-known singular UV-IR mixing. A new planar limit of the fuzzy sphere is defined in which the noncomm…
We study IR/UV mixing effects in noncommutative supersymmetric Yang-Mills theories with gauge group U(N) using background field perturbation theory. We compute three- and four-point functions of background fields, and show that the IR/UV mixed contributions to these correlators can be reproduced from an explicitly gauge-invariant effective action, which is expressed in terms of open Wilson lines.
In this paper we study the phenomenon of UV/IR mixing in noncommutative field theories from the point of view of world-sheet open-closed duality in string theory. New infrared divergences in noncommutative field theories arise as a result of integrating over high momentum modes in the loops. These are believed to come from integrating out additional bulk closed string modes. We analyse this issue in detail for the bosonic theory and further for the supersymmetric theory on the $C^2/Z_2$ orbifold. We elucidate on the exact role played by the constant background $B$-field in this correspondence.
We study the quantum mechanical consistency of noncommutative gauge theories by perturbatively analyzing the Wilsonian quantum effective action in the matrix formulation. In the process of integrating out UV states, we find new divergences having dual UV-IR interpretations and no analogues in ordinary quantum field theories. The appearance of these new UV-IR divergences has profound consequences for the renormalizability of the theory. In particular, renormalizability fails in any nonsupersymmetric noncommutative gauge theory. In fact, we argue that renormalizability generally fails in any non…
We consider noncommutative analogs of scalar electrodynamics and N=2 D=4 SUSY Yang-Mills theory. We show that one-loop renormalizability of noncommutative scalar electrodynamics requires the scalar potential to be an anticommutator squared. This form of the scalar potential differs from the one expected from the point of view of noncommutative gauge theories with extended SUSY containing a square of commutator. We show that fermion contributions restore the commutator in the scalar potential. This provides one-loop renormalizability of noncommutative N=2 SUSY gauge theory. We demonstrate a pre…
Noncommutative IR singularities and UV/IR mixing in relation with the Goldstone theorem for complex scalar field theory are investigated. The classical model has two coupling constants, $λ_1$ and $λ_2$, associated to the two noncommutative extensions $ϕ^*\starϕ\starϕ^*\starϕ$ and $ϕ^*\starϕ^*\starϕ\starϕ$ of the interaction term $|ϕ|^4$ on commutative spacetime. It is shown that the symmetric phase is one-loop renormalizable for all $λ_1$ and $λ_2$ compatible with perturbation theory, whereas the broken phase is proved to exist at one loop only if $λ_2=0$, a condition required by the Ward iden…
We study infrared divergences due to ultraviolet-infrared mixing in quantum field theory on Moyal space with Lorentzian signature in the Yang-Feldman formalism. Concretely, we are considering the phi^4 and the phi^3 model in arbitrary even dimension. It turns out that the situation is worse than in the Euclidean setting, in the sense that we find infrared divergences in graphs that are finite there. We briefly discuss the problems one faces when trying to adapt the nonlocal counterterms that render the Euclidean model renormalizable.
In this thesis I study various aspects of theories in the two most studied examples of noncommutative spacetimes: canonical spacetime ($[x_μ,x_ν]=θ_{μν}$) and $κ$-Minkowski spacetime ($[x_{i},t]=κ^{-1} x_{i}$). In the first part of the thesis I consider the description of the propagation of "classical" waves in these spacetimes. In the case of $κ$-Minkowski this description is rather nontrivial, and its phenomenological implications are rather striking. In the second part of the thesis I examine the structure of quantum field theory in noncommutative spacetime, with emphasis on the simple case…
We explicitly evaluate one-loop (annulus) planar and nonplanar open string amplitudes in the presence of the background NS-NS two-form field. In the decoupling limit of Seiberg and Witten, we find that the nonplanar string amplitudes reproduce the UV/IR mixing of noncommutative field theories. In particular, the investigation of the UV regime of the open string amplitudes shows that certain IR closed string degrees of freedom survive the decoupling limit as previously predicted from the noncommutative field theory analysis. These degrees of freedom are responsible for the quadratic, linear and…
In this report we show that neutrino mixing is intrinsically contained in Connes' noncommutative spectral geometry construction, thanks to the introduction of the doubling of algebra, which is connected to the Bogoliubov transformation. It is known indeed that these transformations are responsible for the mixing, turning the mass vacuum state into the flavor vacuum state, in such a way that mass and flavor vacuum states are not unitary equivalent. There is thus a red thread that binds the doubling of algebra of Connes' model to the neutrino mixing.
Noncommutative ${\cal N}=1$ and ${\cal N}=2$ supersymmetric Yang-Mills theories with gauge group U(N) are studied here using the background field method and superspace background covariant D-algebra in perturbation theory. At one loop divergences arise only in the two-point functions. They are logarithmic UV/IR divergences in the planar/nonplanar sectors that play a role dual to each other. We compute the planar and non planar contributions to the three- and four-point functions with vector external lines. We find that the three-point function vanishes, while the four-point function receives c…
We investigate some issues that are relevant for the derivation of experimental limits on the parameters of canonical noncommutative spacetimes. By analyzing a simple Wess-Zumino-type model in canonical noncommutative spacetime with soft supersymmetry breaking we explore the implications of ultraviolet supersymmetry on low-energy phenomenology. The fact that new physics in the ultraviolet can modify low-energy predictions affects significantly the derivation of limits on the noncommutativity parameters based on low-energy data. These are, in an appropriate sense here discussed, ``conditional l…
We show that allowing the metric dimension of a space to be independent of its KO-dimension and turning the finite noncommutative geometry F-- whose product with classical 4-dimensional space-time gives the standard model coupled with gravity--into a space of KO-dimension 6 by changing the grading on the antiparticle sector into its opposite, allows to solve three problems of the previous noncommutative geometry interpretation of the standard model of particle physics: The finite geometry F is no longer put in "by hand" but a conceptual understanding of its structure and a classification of it…
In this article we calculate several divergent amplitudes in phi^4-theory on non-commutative space-time in the framework of Interaction Point Time Ordered Perturbation Theory (IPTOPT), continuing work done in hep-th/0209253. On the ground of these results we find corresponding Feynman rules which allow for a much easier diagrammatic calculation of amplitudes. The most important feature of the present theory is the lack of the UV/IR mixing problem in all amplitudes calculated so far. Although we are not yet able to give a rigorous proof, we provide a strong argument for this result to hold in g…
We study the perturbative dynamics of noncommutative field theories on R^d, and find an intriguing mixing of the UV and the IR. High energies of virtual particles in loops produce non-analyticity at low momentum. Consequently, the low energy effective action is singular at zero momentum even when the original noncommutative field theory is massive. Some of the nonplanar diagrams of these theories are divergent, but we interpret these divergences as IR divergences and deal with them accordingly. We explain how this UV/IR mixing arises from the underlying noncommutativity. This phenomenon is rem…
Using background field perturbation theory we study Wilsonian effective actions of noncommutative gauge theories with an arbitrary matter content. We determine the Wilsonian coupling constant and the gauge boson polarization tensor as functions of the momentum scale k at the one-loop level and study their short-distance behaviour as theta k ->0, where theta is the noncommutativity parameter. The mixing between the short-distance and the long-distance degrees of freedom characteristic of noncommutative field theories violates the universality of the Wilsonian action and leads to IR-singularitie…
The recent extension of the standard model to include massive neutrinos in the framework of noncommutative geometry and the spectral action principle involves new scalar fields and their interactions with the usual complex scalar doublet. After ensuring that they bring no unphysical consequences, we address the question of how these fields affect the physics predicted in Weinberg-Salam theory, particularly in the context of the Electroweak phase transition. Applying the Dolan-Jackiw procedure, we calculate the finite temperature corrections, and find that the phase transition is first order. T…
It is shown that the mixing of ultraviolet and infrared divergences in quantum field theory on Moyal space is not an artefact of the Euclidean framework, but occurs also in the Hamiltonian setting when the interaction is given in terms of the Moyal twisted convolution product. The mixing mechanism in both settings is examined from the point of view of microlocal analysis and it is shown that they are different from one another.
We study the coupling of fermions to Yang-Mills matrix models in the framework of emergent noncommutative gravity. It is shown that the matrix model action provides an appropriate coupling for fermions to gravity, albeit with a non-standard spin-connection. Integrating out the fermions in a nontrivial geometrical background induces indeed the Einstein-Hilbert action for on-shell geometries plus a dilaton-like term. This result explains UV/IR mixing as a gravity effect. It also illuminates why UV/IR mixing remains even in supersymmetric models, except in the N=4 case.
We start by discussing the classical noncommutative (NC) Q-ball solutions near the commutative limit, then generalize the virial relation. Next we quantize the NC Q-ball canonically. At very small theta quantum correction to the energy of the Q-balls is calculated through summation of the phase shift. UV/IR mixing terms are found in the quantum corrections which cannot be renormalized away. The same method is generalized to the NC GMS soliton for the smooth enough solution. UV/IR mixing is also found in the energy correction and UV divergence is shown to be absent. In this paper only (2+1) dim…
We assume that the noncommutativity starts to be visible continuously from a scale $Λ_{NC}$. According to this assumption, a two-loop effective action is derived for noncommutative $ϕ^{4}$ and $ϕ^{3}$ theories from a Wilsonian point of view. We show that these effective theories are free of UV/IR mixing phenomena. We also investigate the positivity constraint on coefficients of higher dimension operators present in the effective theory. This constraint makes the low energy theory to be UV completion of a full theory. Finally, we discuss noncommutativity and extra dimensions. In our effective t…
We demonstrate the existence of entanglement between the spatial degrees of freedom of a system of harmonic oscillators placed in the noncommutative Moyal plane ("exotic oscillators") by computing the entanglement entropy as measured by the von Neumann entropy of the reduced density matrix. It is explicitly verified that the entanglement arises from the noncommutativity, which controls the coupling strength between the spatial modes. This can easily be generalised to the case where the momentum components also satisfy noncommutative relations, so that the entire phase space becomes noncommutat…
In this work, I investigate the noncommutative Poisson algebra of classical observables corresponding to a proposed general Noncommutative Quantum Mechanics, \cite{1}. I treat some classical systems with various potentials and some Physical interpretations are given concerning the presence of noncommutativity at large scales (Celeste Mechanics) directly tied to the one present at small scales (Quantum Mechanics) and its possible relation with UV/IR mixing.
We study physical implications of the doubling of the algebra, an essential element in the construction of the noncommutative spectral geometry model, proposed by Connes and his collaborators as offering a geometric explanation for the standard model of strong and electroweak interactions. Linking the algebra doubling to the deformed Hopf algebra, we build Bogogliubov transformations and show the emergence of neutrino mixing.
We study the renormalization of dimension four composite operators and the energy-momentum tensor in noncommutative complex scalar field theory. The proper operator basis is defined and it is proved that the bare composite operators are expressed via renormalized ones with the help of an appropriate mixing matrix which is calculated in the one-loop approximation. The number and form of the operators in the basis and the structure of the mixing matrix essentially differ from those in the corresponding commutative theory and in noncommutative real scalar field theory. We show that the energy-mom…
Motivated by recent discussions of IR/UV mixing in noncommutative field theories, we perform a detailed analysis of the non-planar amplitudes of the bosonic open string in the presence of an external B-field at the one-loop level. We carefully isolate, at the string theory level, the contribution which is responsible for the IR/UV behavior in the field theory limit. We show that it is a pure open string effect by deriving it from the factorization of the one-loop amplitude into the disk amplitudes of intermediate open string insertions. We suggest that it is natural to understand IR/UV mixing …
Within the superfield approach, we prove the absence of UV/IR mixing in the three-dimensional noncommutative supersymmetric Maxwell-Chern-Simons theory at any loop order and demonstrate its finiteness in one, three and higher loop orders.
We revisit the problem of quantizing field theories on noncommutative Moyal spacetime with \emph{light-like} noncommutativity. To tackle the issues arising from noncommuting and hence nonlocal time, we argue that for this case light-front quantization procedure should be employed. In this appropriate quantization scheme we perform the non-planar loop analysis for the light-like noncommutative field theories. One of the important and peculiar features of light-front quantization is that the UV cutoff of the light-cone Hamiltonian manifests itself as an IR cutoff for the light-cone momentum, $p^…
Anomalies arising from nonplanar triangle diagrams of noncommutative gauge theory are studied. Local chiral gauge anomalies for both noncommutative U(1) and U(N) gauge theories with adjoint matter fields are shown to vanish. For noncommutative QED with fundamental matters, due to UV/IR mixing a finite anomaly emerges from the nonplanar contributions. It involves a generalized $\star$-product of gauge fields.
The twist-deformation of the Poincaré algebra as symmetry of the field theories on noncommutative space-time with Heisenberg-like commutation relation is discussed in connection to the relation between a sound approach to the twist and the quantization in noncommutative field theory. The recent claims of violation of Pauli's spin-statistics relation and the absence of UV/IR mixing in such theories are shown not to be founded.
In the absence of gauge fields, quantum field theories on the Groenewold-Moyal (GM) plane are invariant under a twisted action of the Poincare group if they are formulated following [1, 2, 3, 4, 5, 6]. In that formulation, such theories also have no UV-IR mixing [7]. Here we investigate UV-IR mixing in gauge theories with matter following the approach of [3, 4]. We prove that there is UV-IR mixing in the one-loop diagram of the S-matrix involving a coupling between gauge and matter fields on the GM plane, the gauge field being nonabelian. There is no UV-IR mixing if it is abelian.
We analyse the IR-singularities that appear in a noncommutative scalar quantum field theory on $\mathcal{E}_4$. We demonstrate with the help of the quadratic one-loop effective action and an appropriate field redefinition that no IR-singularities exist. No new degrees of freedom are needed to describe the UV/IR-mixing.
Algebraic Yang-Mills-Higgs theories based on noncommutative geometry have brought forth novel extensions of gauge theories with interesting applications to phenomenology. We sketch the model of Connes and Lott, as well as variants of it, and the model developed by a Mainz-Marseille group, by comparing them in a schematic way. The role of fermion masses and mixings is discussed, and the question of possible parameter relations is briefly touched.
We consider the noncommutative hypermultiplet model within harmonic superspace approach. The 1-loop four-point contributions to the effective action of selfinteracting q-hypermultiplet are computed. This model has two coupling constants instead of a single one in commutative case. It is shown that both these coupling constants are generated by 1-loop quantum corrections in the model of q-hypermultiplet interacting with vector multiplet. The holomorphic effective action of q-hypermultiplet in external gauge superfield is calculated. For the fundamental representation there is no UV/IR-mixing an…
A formulation of (non-anticommutative) N=1/2 supersymmetric U(N) gauge theory in noncommutative space is studied. We show that at one loop UV/IR mixing occurs. A generalization of Seiberg-Witten map to noncommutative and non-anticommutative superspace is employed to obtain an action in terms of commuting fields at first order in the noncommutativity parameter tetha. This leads to abelian and non-abelian gauge theories whose supersymmetry transformations are local and non-local, respectively.
We show that the noncommutative Wess-Zumino model is renormalizable to all orders of perturbation theory. The noncommutative scalar potential by itself is non-renormalizable but the Yukawa terms demanded by supersymmetry improve the situation turning the theory into a renormalizable one. As in the commutative case, there are neither quadratic nor linear divergences. Hence, the IR/UV mixing does not give rise to quadratic infrared poles.
Motivated by the mixing of UV and IR effects, we test the OPE formula in noncommutative field theory. First we look at the renormalization of local composite operators, identifying some of their characteristic IR/UV singularities. Then we find that the product of two fields in general cannot be described by a series expansion of single local operator insertions.
It is well established that the $SU(P)_L$ gauge symmetry for $P\geq 3$ can address the question of fermion generation number due to the anomaly cancellation, but it neither commutes nor closes algebraically with electric and baryon-minus-lepton charges. Hence, two $U(1)$ factors that determine such charges are required, yielding a complete gauge symmetry, $SU(P)_L\otimes U(1)_X\otimes U(1)_N$, apart from the color group. The resulting theory manifestly provides neutrino mass, dark matter, inflation, and baryon asymmetry of the universe. Furthermore, this gauge structure may present kinetic mix…
We study the one loop dynamics of QFT on the fuzzy sphere and calculate the planar and nonplanar contributions to the two point function at one loop. We show that there is no UV/IR mixing on the fuzzy sphere. The fuzzy sphere is characterized by two moduli: a dimensionless parameter N and a dimensionful radius R. Different geometrical phases can obtained at different corners of the moduli space. In the limit of the commutative sphere, we find that the two point function is regular without UV/IR mixing; however quantization does not commute with the commutative limit, and a finite ``noncommutat…
We review recent results on twisted noncommutative quantum field theory by embedding it into a general framework for the quantization of systems with a twisted symmetry. We discuss commutation relations in this setting and show that the twisted structure is so rigid that it is hard to derive any predictions, unless one gives up general principles of quantum theory. It is also shown that the twisted structure is not responsible for the presence or absence of UV/IR-mixing, as claimed in the literature.
We study in one-loop perturbation theory noncommutative fuzzy quenched QED_4. We write down the effective action on fuzzy S**2 x S**2 and show the existence of a gauge-invariant UV-IR mixing in the model in the large N planar limit. We also give a derivation of the beta function and comment on the limit of large mass of the normal scalar fields. We also discuss topology change in this 4 fuzzy dimensions arising from the interaction of fields (matrices) with spacetime through its noncommutativity.
Refining previous work by Iso, Kawai and Kitazawa, we discuss bi-local string states as a tool for loop computations in noncommutative field theory and matrix models. Defined in terms of coherent states, they exhibit the stringy features of noncommutative field theory. This leads to a closed form for the 1-loop effective action in position space, capturing the long-range non-local UV/IR mixing for scalar fields. The formalism applies to generic fuzzy spaces. The non-locality is tamed in the maximally supersymmetric IKKT or IIB model, where it gives rise to supergravity. The linearized supergra…
Field theories on deformed spaces suffer from the IR/UV mixing and renormalization is generically spoiled. In work with R. Wulkenhaar, one of us realized a way to cure this disease by adding one more marginal operator. We review these ideas, show the application to $ϕ^3$ models and use the heat kernel expansion methods for a scalar field theory coupled to an external gauge field on a $θ$-deformed space and derive noncommutative gauge field actions.
In formulating gauge field theories on noncommutative (NC) spaces it is suggested that particles carrying gauge invariant quantities should not be viewed as pointlike, but rather as extended objects whose sizes grow linearly with their momenta. This and other generic properties deriving from the nonlocal character of interactions (showing thus unambiguously their quantum-gravity origin) lead to a specific form of UV/IR mixing as well as to a pathological behavior at the quantum level when the noncommutativity parameter theta is set to be arbitrarily small. In spite of previous suggestions that…
We study the low-energy dynamics of noncommutative $\N=2$ supersymmetric U(N) Yang-Mills theories in the Coulomb phase. Exact results are derived for the leading terms in the derivative expansion of the Wilsonian effective action. We find that in the infrared regime the U(1) subgroup decouples, and the remaining SU(N) is described by the ordinary commutative Seiberg-Witten solution. IR/UV mixing is present in the U(1), but not in SU(N). Our analysis is based on explicit perturbative and multi-instanton calculations.
We present a noncommutative gauge theory that has the ordinary Standard Model as its low-energy limit. The model is based on the gauge group U(4) x U(3) x U(2) and is constructed to satisfy the key requirements imposed by noncommutativity: the UV/IR mixing effects, restrictions on representations and charges of matter fields, and the cancellation of noncommutative gauge anomalies. At energies well below the noncommutative mass scale our model flows to the commutative Standard Model plus additional free U(1) degrees of freedom which are decoupled due to the UV/IR mixing. Our model also predicts…
In this work we propose the Z -> gamma gamma decay as a process strictly forbidden in the standard model, suitable for the search of noncommutativity of coordinates at very short distances. We computed the Z -> gamma gamma partial width in the framework of the recently proposed one-loop renormalizable gauge sector of the noncommutative standard model. New experimental possibilities at LHC are analyzed and a firm bound to the scale of noncommutativity parameter is set around 1 TeV.
Treating hadronic flavor symmetries with quantum algebras U_q(su_n) leads to interesting consequences such as: new mass sum rules for hadrons 1^-, (1/2)^+, (3/2)^+ of improved accuracy; possibility to label different flavors topologically - by torus winding number; properly fixed deformation parameter q in case of baryons is linked in a simplest way to the Cabibbo angle θ_C, that suggests for θ_C the exact value π/{14}. In this connection, we discuss the possibility that this angle and the Cabibbo mixing as a whole take its origin in noncommutativity of some additional, with regard to 3+1, spa…
We consider the noncommutative space $\mathbb{R}^3_λ$, a deformation of the algebra of functions on $\mathbb{R}^3$ which yields a "foliation" of $\mathbb{R}^3$ into fuzzy spheres. We first construct a natural matrix base adapted to $\mathbb{R}^3_λ$. We then apply this general framework to the one-loop study of a two-parameter family of real-valued scalar noncommutative field theories with quartic polynomial interaction, which becomes a non-local matrix model when expressed in the above matrix base. The kinetic operator involves a part related to dynamics on the fuzzy sphere supplemented by a t…
In this paper, we establish the analysis of noncommutative Yukawa theory, encompassing neutral and charged scalar fields. We approach the analysis by considering carefully the derivation of the respective effective actions. Hence, based on the obtained results, we compute the one-loop contributions to the neutral and charged scalar field self-energy, as well as to the Chern-Simons polarization tensor. In order to properly define the behaviour of the quantum fields, the known UV/IR mixing due to radiative corrections is analysed in the one-loop physical dispersion relation of the scalar and gau…
We study a self-interacting scalar $φ^4$ theory on the $d$-dimensional noncommutative torus. We determine, for the particular cases $d=2$ and $d=4$, the counterterms required by one-loop renormalization. We discuss higher loops in two dimensions and two-loop contributions to the self-energy in four dimensions. Our analysis points toward the absence of any problems related to the UV/IR mixing and thus to renormalizability of the theory. However, we find another potentially troubling phenomenon which is a wild behavior of the two-point amplitude as a function of the noncommutativity matrix $θ$.
The one-loop contribution to vacuum polarization is calculated for the adjoint fermions in three dimensional noncommutative spaces, both at zero and finite temperature. At zero temperature, we confirm a previously found result for the parity odd part and subsequently analyze the even parity part, which exhibits UV/IR mixing. We discuss in detail, two regimes of the high temperature behavior of the parity odd part. When the thermal wavelength is much smaller, as compared to the noncommutativity scale, we find an interesting Fermi-Bose transmutation in the nonplanar part.
Fermions coupled to Yang-Mills matrix models are studied from the point of view of emergent gravity. We show that the simple matrix model action provides an appropriate coupling for fermions to gravity, albeit with a non-standard spin connection. Integrating out the fermions in a nontrivial geometrical background induces indeed the Einstein-Hilbert action and a dilaton-like term, at least for on-shell geometries. This explains and precisely reproduces the UV/IR mixing for fermions in noncommutative gauge theory, extending recent results for scalar fields. It also explains why some UV/IR mixing…
