TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.9.5.063
TI  - An exact mapping between loop-erased random walks and an interacting field theory with two fermions and one boson
PY  - 2020/11/04
UR  - https://www.scipost.org/SciPostPhys.9.5.063
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 9
IS  - 5
SP  - 063
A1  - Shapira, Assaf
AU  - Wiese, Kay Joerg
AB  - We give a simplified proof for the equivalence of loop-erased random walks to a lattice model containing two complex fermions, and one complex boson. This equivalence works on an arbitrary directed graph. Specifying to the $d$-dimensional hypercubic lattice, at large scales this theory reduces to a scalar $\phi^4$-type theory with two complex fermions, and one complex boson. While the path integral for the fermions is the Berezin integral, for the bosonic field we can either use a complex field $\phi(x)\in \mathbb C$ (standard formulation) or a nilpotent one satisfying $\phi(x)^2 =0$. We discuss basic properties of the latter formulation, which has distinct advantages in the lattice model.
ER  -

@Article{10.21468/SciPostPhys.9.5.063,
	title={{An exact mapping between loop-erased random walks and an interacting field theory with two fermions and one boson}},
	author={Assaf Shapira and Kay Jörg Wiese},
	journal={SciPost Phys.},
	volume={9},
	pages={063},
	year={2020},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.9.5.063},
	url={https://scipost.org/10.21468/SciPostPhys.9.5.063},
}