Sandpiles, loop-erased random walks, depinning of CDW, and the O(n) model at n=-2. How are they all related?

Imagine an ant starting at its nest (black dot to the left), walking around randomly (trace detectable by smell, in red) until it finds food (green dot to the right). A second ant may follow efficiently: Instead of walking randomly on the red trace, whenever it encounters a crossing, it follows the youngest trace (strongest smell), effectively erasing the superfluous loops. Mathematicians call the resulting object (blue) a loop erased random walk (LERW). By construction, it is non-self-intersecting. 

While ants probably use only an approximation to this trick, we have been able to prove mathematically that the theory behind is equivalent to an interacting theory with two fermions and one boson, or the n-vector model in the unusual limit of  n=-2 components. These models are themselves equivalent to charge-density waves at depinning, Laplacian growth (describing electric discharges), Abelian sandpiles (the key model of self-organised criticality), uniform spanning trees, and the Potts model with q=0 states. The talk will discuss some of the key relations, and how they are imbedded into the functional renormalization group picture of disordered elastic manifolds. 

References;
[1] K.J. Wiese and A.A. Fedorenko, Nucl. Phys. B 946 (2019) 114696, arXiv:1802.08830.
[2] K.J. Wiese and A.A. Fedorenko, Phys. Rev. Lett. 123 (2019) 197601, arXiv:1908.11721 
[3] A. Shapira and K.J. Wiese, SciPost Phys. 9 (2020) 063, arXiv:2006.07899.
[4] K.J. Wiese, Theory and experiments for disordered elastic manifolds, 
    depinning, avalanches, and sandpiles, (2021), arXiv:2102.01215.