Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Global Renormalization Group Trajectory in a Critical Supersymmetric
  Field Theory on the Lattice Z^3   We consider an Euclidean supersymmetric field theory in $Z^3$ given by a
supersymmetric $\Phi^4$ perturbation of an underlying massless Gaussian measure
on scalar bosonic and Grassmann fields with covariance the Green's function of
a (stable) L\'evy random walk in $Z^3$. The Green's function depends on the
L\'evy-Khintchine parameter $\alpha={3+\epsilon\over 2}$ with $0<\alpha<2$. For
$\alpha ={3\over 2}$ the $\Phi^{4}$ interaction is marginal. We prove for
$\alpha-{3\over 2}={\epsilon\over 2}>0$ sufficiently small and initial
parameters held in an appropriate domain the existence of a global
renormalization group trajectory uniformly bounded on all renormalization group
scales and therefore on lattices which become arbitrarily fine. At the same
time we establish the existence of the critical (stable) manifold. The
interactions are uniformly bounded away from zero on all scales and therefore
we are constructing a non-Gaussian supersymmetric field theory on all scales.
The interest of this theory comes from the easily established fact that the
Green's function of a (weakly) self-avoiding L\'evy walk in $Z^3$ is a second
moment (two point correlation function) of the supersymmetric measure governing
this model. The control of the renormalization group trajectory is a
preparation for the study of the asymptotics of this Green's function. The
rigorous control of the critical renormalization group trajectory is a
preparation for the study of the critical exponents of the (weakly)
self-avoiding L\'evy walk in $Z^3$.

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The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
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The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
3
The categories of this paper are: physics