Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fermionic field theory for trees and forests   We prove a generalization of Kirchhoff's matrix-tree theorem in which a large
class of combinatorial objects are represented by non-Gaussian Grassmann
integrals. As a special case, we show that unrooted spanning forests, which
arise as a q \to 0 limit of the Potts model, can be represented by a Grassmann
theory involving a Gaussian term and a particular bilocal four-fermion term. We
show that this latter model can be mapped, to all orders in perturbation
theory, onto the N-vector model at N=-1 or, equivalently, onto the sigma-model
taking values in the unit supersphere in R^{1|2}. It follows that, in two
dimensions, this fermionic model is perturbatively asymptotically free.

33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph