From quark and nucleon correlations to discrete symmetry and clustering in nuclei

Starting with a quark model of nucleon structure in which the valence quarks are strongly correlated within a nucleon, the light nuclei are constructed by assuming similar correlations of the quarks of neighboring nucleons. Applying the model to larger collections of nucleons reveals the emergence of the face-centered cubic (FCC) symmetry at the nuclear level. Nuclei with closed shells possess octahedral symmetry. Binding of nucleons are provided by quark loops formed by three and four nucleon correlations. Quark loops are responsible for formation of exotic (borromean) nuclei, as well. The model unifies independent particle (shell) model, liquid-drop and cluster models.Comment: 12 pages, 4 figures. Presented at Int. Symp. "Exotic Nuclei - Exon 2016

RG stability of integrable fishnet models

We address the question of perturbative consistency in the scalar fishnet models presented by Caetano, Gurdogan and Kazakov\cite{Gurdogan:2015csr, Caetano:2016ydc}. We argue that their 3-dimensional $\phi^{6}$ fishnet model becomes perturbatively stable under renormalization in the large $N$ limit, in contrast to what happens in their 4-dimensional $\phi^{4}$ fishnet model, in which double trace terms are known to be generated by the RG flow. We point out that there is a direct way to modify this second theory that protects it from such corrections. Additionally, we observe that the 6-dimensional $\phi^{3}$ Lagrangian that spans an hexagonal integrable scalar fishnet is consistent at the perturbative level as well. The nontriviality and simplicity of this last model is illustrated by computing the anomalous dimensions of its $\text{tr}\phi_i \phi_j$ operators to all perturbative orders.Comment: 25 pages, 15 figures. V2: Added references, minor correction

Towards a full solution of the large N double-scaled SYK model

We compute the exact, all energy scale, 4-point function of the large $N$ double-scaled SYK model, by using only combinatorial tools and relating the correlation functions to sums over chord diagrams. We apply the result to obtain corrections to the maximal Lyapunov exponent at low temperatures. We present the rules for the non-perturbative diagrammatic description of correlation functions of the entire model. The latter indicate that the model can be solved by a reduction of a quantum deformation of SL$(2)$, that generalizes the Schwarzian to the complete range of energies.Comment: 52+28 pages, 14 figures; v2: references revised, typos corrected, changed normalization of SL(2)_q 6j symbo