Commutative limit of a renormalizable noncommutative model

Renormalizable $\phi^{\star 4}_4$ models on Moyal space have been obtained by modifying the commutative propagator. But these models have a divergent "naive" commutative limit. We explain here how to obtain a coherent such commutative limit for a recently proposed translation-invariant model. The mechanism relies on the analysis of the uv/ir mixing in general Feynman graphs.Comment: 11 pages, 3 figures, minor misprints being correcte

One-loop effects in a self-dual planar noncommutative theory

We study the UV properties, and derive the explicit form of the one-loop effective action, for a noncommutative complex scalar field theory in 2+1 dimensions with a Grosse-Wulkenhaar term, at the self-dual point. We also consider quantum effects around non-trivial minima of the classical action which appear when the potential allows for the spontaneous breaking of the U(1) symmetry. For those solutions, we show that the one-loop correction to the vacuum energy is a function of a special combination of the amplitude of the classical solution and the coupling constant.Comment: Version to appear in JHE

Loop quantum gravity: the first twenty five years

This is a review paper invited by the journal "Classical ad Quantum Gravity" for a "Cluster Issue" on approaches to quantum gravity. I give a synthetic presentation of loop gravity. I spell-out the aims of the theory and compare the results obtained with the initial hopes that motivated the early interest in this research direction. I give my own perspective on the status of the program and attempt of a critical evaluation of its successes and limits.Comment: 24 pages, 3 figure