Renormalization on the fuzzy sphere
May 29, 2019
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.
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