Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tensor Field Theories: Renormalization and Random Geometry   This thesis focuses on renormalization of quantum field theories. Its first
part considers three tensor models in three dimensions, a Fermionic quartic
with tensors of rank-3 and two Bosonic sextic, of ranks 3 and 5. We rely upon
the large-$N$ melonic expansion of tensor models. For the first model,
invariant under $U(N)^3$, we obtain the RG flow of the two melonic couplings
and the vacuum phase diagram, from a reformulation with a diagonalizable matrix
intermediate field. The discrete chiral symmetry breaks spontaneously and we
compare with the three-dimensional Gross-Neveu model. Beyond the massless
$U(N)^3$ symmetric phase, we also observe a massive phase of same symmetry and
another where the symmetry breaks into $U(N^2)\times U(N/2)\times U(N/2)$. A
matrix model invariant under $U(N)\times U(N^2)$, with close properties, is
also studied. For the other models, with symmetry groups $U(N)^3$ and $O(N)^5$,
a non-melonic coupling (the "wheel") with an optimal scaling in $N$ drives us
to a generalized melonic expansion. The kinetic terms are taken of short- and
long-range, and we analyze perturbatively, at large-$N$, the RG flows of the
sextic couplings up to four loops. Only the rank-3 model displays non-trivial
fixed points (two real Wilson-Fisher-like in the short-range case and a line of
fixed points in the other). We finally obtain the real conformal dimensions of
the primary bilinear operators. In the second part, we establish the first
results of perturbative multi-scale renormalization for a quartic scalar field
on critical Galton-Watson trees, with a long-range kinetic term. At
criticality, an emergent infinite spine provides a space of effective dimension
$4/3$ on which to compute averaged correlation fonctions. This approach
formalizes the notion of a QFT on a random geometry. We use known probabilistic
bounds on the heat-kernel on a random graph reviewed in detail.

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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: chem-ph