  The SYK model proposed by Sachdev, Ye, and Kitaev consists of Majorana
fermions that interact randomly four at a time. The model develops a dense
spectrum above the ground state, due to which the model becomes nearly
conformal. This suggests that a holographic dual may exist, which makes the SYK
model interesting in the study of quantum gravity. It has been found that the
SYK model is similar to large $N$ tensor models: in both models, only the
melonic diagrams survive in the large $N$ limit. In this thesis, we explore the
large $N$ tensor model with $O(N)^3$ symmetry containing two flavors of
Majorana fermions in the fundamental representation. Its quartic Hamiltonian
depends on a real parameter $\beta$. We derive the kernels of the four point
functions. With the spectra that we find from the kernels, we calculate the
scaling dimensions of several types of conformal primaries. We also find a
duality relation between two Hamiltonians of different values of $\beta$. This
is not a perfect duality, because the normalization of energy scales with the
transformation. Nevertheless, the ratios of the energies are the same, and the
operator dimensions are preserved. In addition, we discover that for $\beta >
1$ or $\beta < 0$ the scaling dimensions of one of the conformal primaries
become complex, rendering the model unstable.
