193 research outputs found
Minimal Connectivity
A k-connected graph such that deleting any edge / deleting any vertex /
contracting any edge results in a graph which is not k-connected is called
minimally / critically / contraction-critically k-connected. These three
classes play a prominent role in graph connectivity theory, and we give a brief
introduction with a light emphasis on reduction- and construction theorems for
classes of k-connected graphs.Comment: IMADA-preprint-math, 33 page
Flowing in Group Field Theory Space: a Review
We provide a non-technical overview of recent extensions of renormalization
methods and techniques to Group Field Theories (GFTs), a class of
combinatorially non-local quantum field theories which generalize matrix models
to dimension . More precisely, we focus on GFTs with so-called
closure constraint, which are closely related to lattice gauge theories and
quantum gravity spin foam models. With the help of recent tensor model tools, a
rich landscape of renormalizable theories has been unravelled. We review our
current understanding of their renormalization group flows, at both
perturbative and non-perturbative levels
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