Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · hep-th/0603052

A nontrivial solvable noncommutative ϕ^3 model in 4 dimensions

H. Grosse·H. Steinacker
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the quantization of the noncommutative selfdual ϕ^3 model in 4 dimensions, by mapping it to a Kontsevich model. The model is shown to be renormalizable, provided one additional counterterm is included compared to the 2-dimensional case which can be interpreted as divergent shift of the field ϕ. The known results for the Kontsevich model allow to obtain the genus expansion of the free energy and of any n-point function, which is finite for each genus after renormalization. No coupling constant or wavefunction renormalization is required. A critical coupling is determined, beyond which the model is unstable. This provides a nontrivial interacting NC field theory in 4 dimensions.

Explore related subjects

hep-thmath-phmath.MP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

H. Grosse, H. Steinacker. 2006-05-24. A nontrivial solvable noncommutative ϕ^3 model in 4 dimensions. https://doi.org/10.1088/1126-6708%2F2006%2F08%2F008

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Analytic approaches to anisotropic holographic superfluids in asymptotically hyperscaling violation geometry

We explore anisotropic holographic superfluidity and find analytic solutions near critical point where superfluid/normalfluid phase transition appears in a holographic dual fluid system. In arXiv:hep-th/1109.4592, the authors obtained such an analytic solution in 5-dimensional Einstein-SU(2)Yang-Mills system, and it is asymptotically AdS$_5$. What is more in this note is that we get analytic solutions near the critical point in 3- and 4- dimensional Einstein-Scalar-U(1)$\times$SU(2)Yang-Mills systems, which become asymptotically hyperscaling violation geometry. We also get leading order back reactions to the background geometry, which clearly shows spatial anisotropy of the bulk geometry. To explore the properties of the spacetime, we compute holographic entanglement entropy and confirm that the superfluid/normalfluid phase transition must occur at the critical point.

hep-th↗
arXiv2026

Bootstrapping transport in the Drude-Kadanoff-Martin model

The Drude-Kadanoff-Martin model is a simple low energy and long wavelength description of charge transport, parameterised by the current relaxation timescale $τ$, charge diffusivity $D$ and charge compressibility $χ$. We obtain sharp constraints on these parameters in terms of the microscopic energy and length scales of any underlying lattice model with local and bounded interactions. Our primary tools are upper bounds on the retarded Green's function for the charge density in such a setting. We first note that the Drude-Kadanoff-Martin model cannot pertain at microscopic energy scales because it is inconsistent with the exponential suppression of spectral weight at the highest frequencies in a lattice model. Secondly, under the assumption that the low energy dynamics is captured by the model, we obtain a lower bound on the collective mean free path $\ell \equiv \sqrt{τD}$. This bound is shown to imply a version of the Mott-Ioffe-Regel bound: systems with $\ell$ much shorter than the lattice length scale cannot have conventional Drude peaks, in the sense of being captured by the DKM model.

hep-th↗
arXiv2026

Gravitational form factors of the proton in the improved holographic QCD model

We compute the gluonic contribution to the gravitational form factors of the proton using the improved holographic QCD model, in which the proton is described in terms of bulk Dirac fermions. Model parameters are constrained using lattice and phenomenological input, allowing us to obtain estimates for the gravitational form factors and to compare them with results from other approaches. Using the extracted form factors, we analyze mechanical properties of the proton, including pressure and shear distributions. We obtain estimates for the mechanical and mass radii of the proton, $ρ_{\text{mech}} \approx 0.63$ fm, $ρ_{\text{mass}} \approx 0.65$ fm, and compare these values with radius estimates from other nonperturbative studies.

hep-th↗