A matrix phase for the phi^4 scalar field on the fuzzy sphere

Details A matrix phase for the phi^4 scalar field on the fuzzy sphere A matrix phase for the phi^4 scalar field on the fuzzy sphere

2004-02-27

arxiv.org/abs/hep-th/0402230v3

JHEP 0404 (2004) 077

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, 10 figures. Axes scales of most figures were corrected. Final version

Scientific paper

10.1088/1126-6708/2004/04/077

The critical properties of the real phi^4 scalar field theory are studied numerically on the fuzzy sphere. The fuzzy sphere is a matrix (non commutative) discretisation of the algebra of functions on the usual two dimensional sphere. It is also one of the simplest examples of a non commutative space to study field theory on. Aside from the usual disordered and uniform phases present in the commutative scalar field theory, we find and discuss in detail a new phase with spontaneously broken rotational invariance, called matrix phase because the geometry of the fuzzy sphere, as expressed by the kinetic term, becomes negligible there. This gives some further insight on the effect of UV-IR mixing, the unusual behaviour which arises naturally when taking the commutative limit of a non commutative field theory.

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