New Phenomena in NC Field Theory and Emergent Spacetime Geometry

Understand

We give a brief review of two nonperturbative phenomena typical of noncommutative field theory which are known to lead to the perturbative instability known as the UV-IR mixing.

• The first phenomena concerns the emergence/evaporation of spacetime geometry in matrix models which describe perturbative noncommutative gauge theory on fuzzy backgrounds.
• In particular we show that the transition from a geometrical background to a matrix phase makes the description of noncommutative gauge theory in terms of fields via the Weyl map only valid below a critical value g_*.
• The second phenomena concerns the appearance of a nonuniform ordered phase in noncommutative scalar \phi^4 field theory and the spontaneous symmetry breaking of translational/rotational invariance which happens even in two dimensions.