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Scalar field theory on the fuzzy two-sphere, represented as a hermitianmatrix model that includes kinetic, mass and quartic interaction terms, isstudied. The effective action in the symmetric large-N regime is analyzed usinga self-consistent bootstrap method which fixes its form up to sixth order inthe eigenvalues and gives a closed expression to all orders in the quadraticinvariant of the matrix, valid close to semicircular distributions. Using thisaction the eigenvalue distribution is calculated for the interacting theory inthe appropriate scaling limit and the phase transition from the disordered tothe symmetric ordered phase is identified, including nonperturbative effects.

Effective action and phase transitions of scalar field on the fuzzy sphere