Abstract
We solve a multitrace matrix model approximating the real quartic scalar field theory on the fuzzy sphere and obtain its phase diagram. We generalize this method to models with modified kinetic terms and demonstrate its use by investigating models related to the removal of the UV/IR mixing. We show that for the fuzzy sphere a modification of the kinetic part of the action by higher derivative term can change the phase diagram of the theory such that the triple point moves further from the origin.
Highlights
Sphere [9,10,11], for the fuzzy disc [12], for the fuzzy sphere with a commutative time, i.e. the three dimensional space R × SF2 [13], for the fuzzy torus [14] and for field on the noncommutative plane coupled to a curvature term [15].1 All these works point to existence of a noncommutative phase of the theory, which breaks the translation invariance of the underlying space
We continue the line of research for the fuzzy sphere started in [31], where the equations describing the second moment matrix model have been solved numerically, the phase diagram with all the three phases has been obtained and the triple point has been identified
The resulting phase diagram for particular values of a and b is shown in the figure 3 and the values of the triple point are given in the table 1
Summary
We provide some essential preliminaries for what follows in further sections. To keep this report as short as possible, we concentrate on the notions and expression we will directly use. A more thorough review of the topics of matrix models and fuzzy field theory can be found in [32,33,34,35,36,37]
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