Week 11.12.2023 – 17.12.2023

We propose a theoretical framework that explains how the mass of simple and higher-order networks emerges from their topology and geometry. We use the discrete topological Dirac operator to define an action for a massless self-interacting topological Dirac field inspired by the Nambu–Jona-Lasinio model. The mass of the network is strictly speaking the mass of this topological Dirac field defined on the network; it results from the chiral symmetry breaking of the model and satisfies a self-consistent gap equation. Interestingly, it is shown that the mass of a network depends on its spectral properties, topology, and geometry. Due to the breaking of the matter–antimatter symmetry observed for the harmonic modes of the discrete topological Dirac operator, two possible definitions of the network mass can be given. For both possible definitions, the mass of the network comes from a gap equation with the difference among the two definitions encoded in the value of the bare mass. Indeed, the bare mass can be determined either by the Betti number β0 or by the Betti number β1 of the network. We provide numerical results on the mass of different networks, including random graphs, scale-free, and real weighted collaboration networks. We also discuss the generalization of these results to higher-order networks, defining the mass of simplicial complexes. The observed dependence of the mass of the considered topological Dirac field with the topology and geometry of the network could lead to interesting physics in the scenario in which the considered Dirac field is coupled with a dynamical evolution of the underlying network structure.

We study Chern-Simons theories at large N with either bosonic or fermionic matter in the fundamental representation. We will show that for smooth conformal line operators, their spectrum and shape dependence can be effectively bootstrapped using minimal inputs.

In this talk, I present new solutions for type IIB supergravity generated by an infinite family of uplifts from six-dimensional supergravity solutions. After compactification on a circle, I will discuss that these backgrounds are proposed to be holographically dual to confining Quantum Field Theories. In the high energies, field theories will approach the strongly coupled regime of 5d quiver gauge field theories. I also mention some observables like Wilson loops and Entanglement entropy to sketch the properties of the theories.

We present a new formulation of string and particle amplitudes that emerges from simple one-dimensional models. The key is a new way to parametrize the positive part of Teichmüller space. The formulation works at all orders in the perturbation series, including non-planar contributions to the amplitudes. The relationship between string and particle amplitudes is made manifest as a "tropical limit". The results are well adapted to studying the scattering of large numbers of particles or amplitudes at high loop order. The talk will in part cover results from arXiv:2309.15913, 2311.09284.