Matrix Models, Belyi Maps, and the Ponzano-Regge Model: A Holographic Hierarchy

The Gaussian
Hermitian matrix model can be viewed as a quantum field theory in zero
dimensions. It provides a mathematical model of gauge-string duality. The string
theory is given by holomorphic Belyi maps from string worldsheets to a 2-sphere
target space.

The matrix model can be reformulated using the fuzzy sphere, which gives a description of the observables in terms of SU(2) spin sums. This leads to a realization of the matrix model correlators in terms of the Ponzano Regge model, which is a theory of Euclidean quantum gravity in three dimensions. This can be interpreted as a membrane version of the string theory, where the string worldsheet naturally lives at the boundary of the 3-manifold.

There is, therefore, a hierarchy of holographies relating the membrane, the Belyi string and the matrix model in three, two and zero dimensions.

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Thursday, June 6, 2013 - 14:30 to 16:00
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