7,216 research outputs found
Noncommutative QFT and Renormalization
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 models and use the heat
kernel expansion methods for a scalar field theory coupled to an external gauge
field on a -deformed space and derive noncommutative gauge field
actions.Comment: To appear in the proceedings of the Workshop "Noncommutative Geometry
in Field and String Theory", Corfu, 2005 (Greece
Induced Gauge Theory on a Noncommutative Space
We discuss the calculation of the 1-loop effective action on four
dimensional, canonically deformed Euclidean space. The theory under
consideration is a scalar model with an additional oscillator
potential. This model is known to be re normalisable. Furthermore, we couple an
exterior gauge field to the scalar field and extract the dynamics for the gauge
field from the divergent terms of the 1-loop effective action using a matrix
basis. This results in proposing an action for noncommutative gauge theory,
which is a candidate for a renormalisable model.Comment: 8 page
Matrix Models, Emergent Gravity, and Gauge Theory
Matrix models of Yang-Mills type induce an effective gravity theory on
4-dimensional branes, which are considered as models for dynamical space-time.
We review recent progress in the understanding of this emergent gravity. The
metric is not fundamental but arises effectively in the semi-classical limit,
along with nonabelian gauge fields. This leads to a mechanism for protecting
certain geometries from corrections due to the vacuum energy.Comment: 8 pages. Based on invited talks given at the Conferences "Quantum
Spacetime and Noncommutative Geometry", Rome, 2008 and at "Workshop on
quantum gravity and nocommutative geometry", Lisbon, 2008 and at "Emergent
Gravity", Boston, 2008 and at DICE2008, Italy, 2008 and at "QG2 2008 Quantum
Geometry and Quantum Gravity", Nottingham, 200
A New Approach to Non-Commutative U(N) Gauge Fields
Based on the recently introduced model of arXiv:0912.2634 for non-commutative
U(1) gauge fields, a generalized version of that action for U(N) gauge fields
is put forward. In this approach to non-commutative gauge field theories, UV/IR
mixing effects are circumvented by introducing additional 'soft breaking' terms
in the action which implement an IR damping mechanism. The techniques used are
similar to those of the well-known Gribov-Zwanziger approach to QCD.Comment: 11 pages; v2 minor correction
Curvature and Gravity Actions for Matrix Models
We show how gravitational actions, in particular the Einstein-Hilbert action,
can be obtained from additional terms in Yang-Mills matrix models. This is
consistent with recent results on induced gravitational actions in these matrix
models, realizing space-time as 4-dimensional brane solutions. It opens up the
possibility for a controlled non-perturbative description of gravity through
simple matrix models, with interesting perspectives for the problem of vacuum
energy. The relation with UV/IR mixing and non-commutative gauge theory is
discussed.Comment: 17 pages; v2+v3: minor correction
On Non-Commutative U*(1) Gauge Models and Renormalizability
Based on our recent findings regarding (non-)renormalizability of
non-commutative U*(1) gauge theories [arxiv:0908.0467, arxiv:0908.1743] we
present the construction of a new type of model. By introducing a soft breaking
term in such a way that only the bilinear part of the action is modified, no
interaction between the gauge sector and auxiliary fields occurs. Demanding in
addition that the latter form BRST doublet structures, this leads to a
minimally altered non-commutative U*(1) gauge model featuring an IR damping
behavior. Moreover, the new breaking term is shown to provide the necessary
structure in order to absorb the inevitable quadratic IR divergences appearing
at one-loop level in theories of this kind. In the present paper we compute
Feynman rules, symmetries and results for the vacuum polarization together with
the one-loop renormalization of the gauge boson propagator and the three-point
functions.Comment: 20 pages, 4 figures; v2-v4: clarified several points, and minor
correction
The One-loop UV Divergent Structure of U(1) Yang-Mills Theory on Noncommutative R^4
We show that U(1) Yang-Mills theory on noncommutative R^4 can be renormalized
at the one-loop level by multiplicative dimensional renormalization of the
coupling constant and fields of the theory. We compute the beta function of the
theory and conclude that the theory is asymptotically free. We also show that
the Weyl-Moyal matrix defining the deformed product over the space of functions
on R^4 is not renormalized at the one-loop level.Comment: 8 pages. A missing complex "i" is included in the field strength and
the divergent contributions corrected accordingly. As a result the model
turns out to be asymptotically fre
Duality covariant quantum field theory on noncommutative Minkowski space
We prove that a scalar quantum field theory defined on noncommutative
Minkowski spacetime with noncommuting momentum coordinates is covariant with
respect to the UV/IR duality which exchanges coordinates and momenta. The proof
is based on suitable resonance expansions of charged noncommutative scalar
fields in a background electric field, which yields an effective description of
the field theory in terms of a coupled complex two-matrix model. The two
independent matrix degrees of freedom ensure unitarity and manifest
CT-invariance of the field theory. The formalism describes an analytic
continuation of the renormalizable Grosse-Wulkenhaar models to Minkowski
signature.Comment: 32 pages; v2: Typos corrected; v3: Further typos corrected - Final
version to appear in JHE
Parametric Representation of Noncommutative Field Theory
In this paper we investigate the Schwinger parametric representation for the
Feynman amplitudes of the recently discovered renormalizable quantum
field theory on the Moyal non commutative space. This
representation involves new {\it hyperbolic} polynomials which are the
non-commutative analogs of the usual "Kirchoff" or "Symanzik" polynomials of
commutative field theory, but contain richer topological information.Comment: 31 pages,10 figure
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