Master Field on Fuzzy Sphere

TL;DR

This paper demonstrates the existence and explicit forms of master fields in the O(N) vector model on both ordinary and fuzzy spheres, highlighting the role of fuzzy sphere cutoff in their construction.

Contribution

It provides explicit forms of master fields on fuzzy spheres and shows their mixing of internal and space-time symmetries, emphasizing the cutoff's importance.

Findings

Master fields exist on both ordinary and fuzzy spheres.

Explicit forms of the master fields are derived.

Fuzzy sphere cutoff is crucial for constructing master fields.

Abstract

The O(N) symmetric vector model is considered on both ordinary and fuzzy sphere. It is shown that in both cases master fields exist and their explicit forms are presented. They are found to mix the internal symmetry and the (fuzzy) space-time symmetry. It is also argued that the cutoff brought by the fuzzy sphere plays an essential role in constructing the master field.