Quantum field theory in a non-commutative space: Theoretical predictions and numerical results on the fuzzy sphere

Panero, Marco

doi:10.3842/SIGMA.2006.081

Quantum field theory in a non-commutative space: Theoretical predictions and numerical results on the fuzzy sphere

Marco Panero
(
- Dublin Inst.
)

Sep, 2006

17 pages

Published in:

SIGMA 2 (2006) 081

e-Print:

hep-th/0609205 [hep-th]

DOI:

10.3842/SIGMA.2006.081

Report number:

DIAS-STP-06-12

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Abstract:

We review some recent progress in quantum field theory in non-commutative space, focusing onto the fuzzy sphere as a non-perturbative regularisation scheme. We first introduce the basic formalism, and discuss the limits corresponding to different commutative or non-commutative spaces. We present some of the theories which have been investigated in this framework, with a particular attention to the scalar model. Then we comment on the results recently obtained from Monte Carlo simulations, and show a preview of new numerical data, which are consistent with the expected transition between two phases characterised by the topology of the support of a matrix eigenvalue distribution.

Non-commutative geometry
differential geometry: noncommutative
field theory: scalar
critical phenomena
sphere: fuzzy
regularization: nonperturbative
numerical calculations

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