Renormalization on the fuzzy sphere
Abstract
We study renormalization on the fuzzy sphere, which is a typical example of non-commutative spaces. We numerically simulate a scalar field theory on the fuzzy sphere, which is described by a Hermitian matrix model. We define correlation functions by using the Berezin symbol and show that they are made independent of the matrix size, which plays a role of a UV cutoff, by tuning one parameter of the theory. We also find that the theories on the phase boundary are universal. They behave as a conformal field theory at short distances, while they universally differ from it at long distances due to the UV/IR mixing.
Cite
@article{arxiv.1811.10806,
title = {Renormalization on the fuzzy sphere},
author = {Kohta Hatakeyama and Asato Tsuchiya and Kazushi Yamashiro},
journal= {arXiv preprint arXiv:1811.10806},
year = {2018}
}
Comments
7 pages, 4 figures, Proceedings of The 36th Annual International Symposium on Lattice Field Theory (Lattice 2018), July 22-28, 2018, East Lansing, Michigan, USA