Motivated by the close connection of tensor models to the SYK model, we use representation theory 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. Finally, we construct a collective field theory description of the bosonic tensor model.

By performing explicit computations of correlation functions, we find evidence that there is a sector of the two matrix model defined by the SU (2) sector of N = 4 super Yang-Mills theory, that can be reduced to eigenvalue dynamics. There is an interesting generalization of the usual Van der Monde determinant that plays a role. The observables we study are the BPS operators of the SU (2) sector and include traces of products of both matrices, which are genuine multi matrix observables. These operators are associated to supergravity solutions of string theory.1 robert@neo.phys.wits.ac.za 2

In 1804, Thomas Young reported the observation of fringes in the intensity of light, and attributed it to the concept of interference between coherent sources. In this paper, we revisit this famous experiment and show how it can easily be demonstrated with digital holography. We look closely at the concept of interference with light and ask, “fringes in what?” We then show that depending on how light interferes, fringe patterns in observables other than intensity can be seen. We explain this conceptually and demonstrate it experimentally. We provide a holistic approach to the topic, aided by modern laboratory practices for a straightforward demonstration of the underlying physics.

In this article we explore the holographic duals of tensor models using collective field theory. We develop a description of the gauge invariant variables of the tensor model. This is then used to develop a collective field theory description of the dynamics. We consider matrix like subsectors that develop an extra holographic dimension. In particular, we develop the collective field theory for the matrix like sector of an interacting tensor model. We check the correctness of the large N collective field by showing that it reproduces the perturbative expansion of large N expectation values. In contrast to this, we argue 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 the 1/N expansion are exhibited. 1 robert@neo.phys.wits.ac.za 2