Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elliptic stochastic quantization   We prove an explicit formula for the law in zero of the solution of a class
of elliptic SPDE in $\mathbb{R}^2$. This formula is the simplest instance of
dimensional reduction, discovered in the physics literature by Parisi and
Sourlas (1979), which links the law of an elliptic SPDE in $d + 2$ dimension
with a Gibbs measure in $d$ dimensions. This phenomenon is similar to the
relation between an $\mathbb{R}^{d + 1}$ dimensional parabolic SPDE and its
$\mathbb{R}^d$ dimensional invariant measure. As such, dimensional reduction of
elliptic SPDEs can be considered a sort of elliptic stochastic quantisation
procedure in the sense of Nelson (1966) and Parisi and Wu (1981). Our proof
uses in a fundamental way the representation of the law of the SPDE as a
supersymmetric quantum field theory. Dimensional reduction for the
supersymmetric theory was already established by Klein et al. (1984). We fix a
subtle gap in their proof and also complete the dimensional reduction picture
by providing the link between the elliptic SPDE and the supersymmetric model.
Even in our $d = 0$ context the arguments are non-trivial and a
non-supersymmetric, elementary proof seems only to be available in the Gaussian
case.

15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph