Non-perturbative string theory dynamics from the gauge / gravity duality

Gossman, David
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Motivated by the close connection of tensor models to the SYK model, and the success of the SYK model within holography, tensor models are studied. A brief introduction to relevant topics surrounding holography and tensor models is given. Representation theory is used to construct the complete set of gauge invariant observables for bosonic and fermionic tensor models. Correlation functions of the gauge invariant operators in the free theory are computed exactly. The gauge invariant operators close a ring. The structure constants of the ring are described explicitly. The holographic duals of tensor models are studied using collective field theory. A description of the gauge invariant variables of the tensor model, is developed. This is used to develop a collective field theory description of the dynamics. A matrixlike subsector that develops an extra holographic dimension is considered. In particular, the collective field theory for the matrix like sector of an interacting tensor model is developed. The correctness of the large N collective field is checked by showing that it reproduces the perturbative expansion of large N expectation values. In contrast to this, it is argued that melonic large N limits do not develop an extra dimension. This conclusion follows from the large N value for the melonic collective field, which has delta function support. The finite N physics of the model is also developed and non-perturbative effects in the1 =N expansion are exhibited
A thesis submitted in fulfilment of the requirements of the degree of Doctor of Philosophy (PhD), Faculty of Science, University of the Witwatersrand