New Phenomena in NC Field Theory and Emergent Spacetime Geometry

TL;DR

This paper reviews nonperturbative phenomena in noncommutative field theory, including emergent spacetime geometry and spontaneous symmetry breaking, highlighting their relation to matrix models and phase transitions.

Contribution

It introduces new insights into the emergence of spacetime and phase transitions in noncommutative field theories through matrix model analysis.

Findings

Spacetime geometry emerges and evaporates in matrix models.

Transition to a matrix phase limits the validity of the Weyl map.

Spontaneous symmetry breaking occurs in noncommutative scalar  theory.

Abstract

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. We argue that this phenomena also originates in the underlying matrix degrees of freedom of the noncommutative field theory. Furthermore it is conjectured that in addition to the usual WF fixed point at $\theta=0$ there must exist a novel fixed point at \theta=\infty corresponding to the quartic hermitian matrix model.