Related papers: A nontrivial solvable noncommutative \phi^3 model …
In the previous study, we formulate a matrix model renormalization group based on the fuzzy spherical harmonics with which a notion of high/low energy can be attributed to matrix elements, and show that it exhibits locality and various…
We develop a general framework for spatial discretisations of parabolic stochastic PDEs whose solutions are provided in the framework of the theory of regularity structures and which are functions in time. As an application, we show that…
We study the correlation functions of a conformally coupled $\phi^4$-interacting theory in AdS$_3$ and its dual CFT$_2$. The one-loop diagram is not expressible in terms of known transcendental functions, but is shown to be expressible as…
We study some of the implications for the perturbative renormalization program when augmented with the Borel-Ecalle resummation. We show the emergence of a new kind of non-perturbative fixed point for the scalar $\phi^4$ model, representing…
In arXiv:math/0105152, the second author used the Kontsevich deformation quantization technique to define a natural connection \omega_n on the compactified configuration spaces of n points on the upper half-plane. This connection takes…
We study renormalized quenched strong-coupling QED in four dimensions in arbitrary covariant gauge. Above the critical coupling leading to dynamical chiral symmetry breaking, we show that there is no finite chiral limit. This behaviour is…
Starting from a self-dual formulation of gravity, we obtain a noncommutative theory of pure Einstein theory in four dimensions. In order to do that, we use Seiberg-Witten map. It is shown that the noncommutative torsion constraint is solved…
We consider the leading order perturbative renormalization of the multicritical $\phi^{2n}$ models and some generalizations in curved space. We pay particular attention to the nonminimal interaction with the scalar curvature $\frac{1}{2}\xi…
We study a noncommutative nonrelativistic fermionic field theory in 2+1 dimensions coupled to the Chern-Simons field. We perform a perturbative analysis of model and show that up to one loop the ultraviolet divergences are canceled and the…
We investigate possible renormalization-group fixed points at nonzero coupling in $\phi^3$ theories in six spacetime dimensions, using beta functions calculated to the four-loop level. We analyze three theories of this type, with (a) a…
The three-dimensional real scalar model, in which the $Z_2$ symmetry spontaneously breaks, is renormalized in a nonperturbative manner based on the Tamm-Dancoff truncation of the Fock space. A critical line is calculated by diagonalizing…
A new nonperturbative approach is used to investigate the Gross-Neveu model of four fermion interaction in the space-time dimensions 2, 3 and 4, the number $N$ of inner degrees of freedom being a fixed integer. The spontaneous symmetry…
We build the two dimensional Gross-Neveu model by a new method which requires neither cluster expansion nor discretization of phase-space. It simply reorganizes the perturbative series in terms of trees. With this method we can for the…
I show that under certain conditions it is possible to define consistent irrelevant deformations of interacting conformal field theories. The deformations are finite or have a unique running scale ("quasi-finite"). They are made of an…
A class of three-dimensional models which satisfy supersymmetric intertwining relations with the simplest - oscillator-like - variant of shape invariance is constructed. It is proved that the models are not amenable to conventional…
We prove that the self-interacting scalar field on the four-dimensional degenerate Moyal plane is renormalisable to all orders when adding a suitable counterterm to the Lagrangean. Despite the apparent simplicity of the model, it raises…
The free Schroedinger theory in d space dimensions is a non-relativistic conformal field theory. The interacting non-linear theory preserves this symmetry in specific numbers of dimensions at the classical (tree) level. This holds in…
UV/IR mixing is one of the most important features of noncommutative field theories. As a consequence of this coupling of the UV and IR sectors, the configuration of fields at the zero momentum limit in these theories is a very singular…
The two-dimensional O(3) nonlinear sigma model is a well known toy model for studying non-perturbative phenomena in quantum field theory. A central challenge is the renormalization of the energy-momentum tensor, which is complicated by the…
A noncommutative Feynman graph is a ribbon graph and can be drawn on a genus $g$ 2-surface with a boundary. We formulate a general convergence theorem for the noncommutative Feynman graphs in topological terms and prove it for some classes…