Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graph duality as an instrument of Gauge-String correspondence   We explore an identity between two branching graphs and propose a physical
meaning in the context of the gauge-gravity correspondence. From the
mathematical point of view, the identity equates probabilities associated with
$\mathbb{GT}$, the branching graph of the unitary groups, with probabilities
associated with $\mathbb{Y}$, the branching graph of the symmetric groups. In
order to furnish the identity with physical meaning, we exactly reproduce these
probabilities as the square of three point functions involving certain
hook-shaped backgrounds. We study these backgrounds in the context of LLM
geometries and discover that they are domain walls interpolating two AdS spaces
with different radii. We also find that, in certain cases, the probabilities
match the eigenvalues of some observables, the embedding chain charges. We
finally discuss a holographic interpretation of the mathematical identity
through our results.

10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con