Spreading of Competing Information in a Network

We propose a simple approach to investigate the spreading of news in a network. In more detail, we consider two different versions of a single type of information, one of which is close to the essence of the information (and we call it good news), and another of which is somehow modified from some biased agent of the system (fake news, in our language). Good and fake news move around some agents, getting the original information and returning their own version of it to other agents of the network. Our main interest is to deduce the dynamics for such spreading, and to analyze if and under which conditions good news wins against fake news. The methodology is based on the use of ladder fermionic operators, which are quite efficient in modeling dispersion effects and interactions between the agents of the system.

The inversion formula and 6j symbol for 3d fermions

In this work we study the 6j symbol of the 3d conformal group for fermionic operators. In particular, we study 4-point functions containing two fermions and two scalars and also those with four fermions. By using weight-shifting operators and harmonic analysis for the Euclidean conformal group, we relate these spinning 6j symbols to the simpler 6j symbol for four scalar operators. As one application we use these techniques to compute 3d mean field theory (MFT) OPE coefficients for fermionic operators. We then compute corrections to the MFT spectrum and couplings due to the inversion of a single operator, such as the stress tensor or a low-dimension scalar. These results are valid at finite spin and extend the perturbative large spin analysis to include non-perturbative effects in spin.

Fermionic response in nonlinear arcsin electrodynamics

We consider certain blackhole solution in non-linear arcsin electrodynamics coupled with gravity and axions. We have studied the behaviour of the fermionic operators in the dual (2+1)-dimensional theory. We consider holographic spectral function for both the backreacted solutions and probe limit over the range of physical parameters. We find that with a variation of the charge density the system changes from Fermi liquid to non-Fermi liquid and the transition point depends on the temperature.