Quantum Field Theory on the q-deformed Fuzzy Sphere

TL;DR

This paper develops a covariant quantum scalar field theory on the q-deformed fuzzy sphere, ensuring smooth classical limits and positivity, and relates it to nonlocal theories on the undeformed sphere via a Drinfeld twist.

Contribution

It introduces a second quantization framework for scalar fields on the q-deformed fuzzy sphere with covariance, positivity, and a connection to nonlocal undeformed theories.

Findings

Quantum field theories are covariant under U_q(su(2))

Theories have a smooth limit as q approaches 1

Equivalent to nonlocal QFTs on the undeformed fuzzy sphere

Abstract

We discuss the second quantization of scalar field theory on the q-deformed fuzzy sphere S^2_{q,N} for q \in \R, using a path-integral approach. We find quantum field theories which are manifestly covariant under U_q(su(2)), have a smooth limit q -> 1, and satisfy positivity and twisted bosonic symmetry properties. Using a Drinfeld twist, they are equivalent to ordinary but slightly "nonlocal" QFT's on the undeformed fuzzy sphere, which are covariant under SU(2).