A matrix phase for the ϕ⁴ scalar field on the fuzzy sphere

Martin, X. (2004) A matrix phase for the ϕ⁴ scalar field on the fuzzy sphere. (Preprint)

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Abstract

The critical properties of the real φ^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.

Item Type: Article
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 19 Jun 2018 13:58
Last Modified: 16 Jul 2018 13:04
URI: http://dair.dias.ie/id/eprint/630

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