Field theory on evolving fuzzy two-sphere

TL;DR

This paper develops a field theory on an evolving fuzzy two-sphere, exploring its properties and continuum limit, revealing a background geometry consistent with the cosmic holographic principle.

Contribution

It introduces a novel field theory framework on an evolving fuzzy sphere, connecting non-commutative geometry with cosmological holographic principles.

Findings

The equations resemble a time-independent form of pure-into-mixed-state evolution.

The theory maintains gauge invariance and conservation laws.

The continuum limit yields a cosmologically relevant background geometry.

Abstract

I construct field theory on an evolving fuzzy two-sphere, which is based on the idea of evolving non-commutative worlds of the previous paper. The equations of motion are similar to the one that can be obtained by dropping the time-derivative term of the equation derived some time ago by Banks, Peskin and Susskind for pure-into-mixed-state evolutions. The equations do not contain an explicit time, and therefore follow the spirit of the Wheeler-de Witt equation. The basic properties of field theory such as action, gauge invariance and charge and momentum conservation are studied. The continuum limit of the scalar field theory shows that the background geometry of the corresponding continuum theory is given by ds^2 = -dt^2+ t d Omega^2, which saturates locally the cosmic holographic principle.