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Boundary correlation functions provide insight into the emergence of aneffective geometry in higher spin gravity duals of O(N) or U(N) symmetric fieldtheories. On a compact manifold, the singlet constraint leads to nontrivialdynamics at finite temperature and large N phase transitions even at vanishing't Hooft coupling. At low temperature, the leading behavior of boundarytwo-point functions is consistent with propagation through a bulk thermal antide Sitter space. Above the phase transition, the two-point function showssignificant departure from thermal AdS space and the emergence of localizedblack hole like objects in the bulk. In adjoint models, these objects appear atlength scales of order of the AdS radius, consistent with a Hawking-Pagetransition, but in vector models they are parametrically larger than the AdSscale. In low dimensions, we find another crossover at large distances beyondwhich the correlation function again takes a thermal AdS form, albeit with atemperature dependent normalization factor.

Probing emergent geometry through phase transitions in free vector and matrix models