Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrability of Conformal Fishnet Theory   We study integrability of fishnet-type Feynman graphs arising in planar
four-dimensional bi-scalar chiral theory recently proposed in arXiv:1512.06704
as a special double scaling limit of gamma-deformed $\mathcal{N}=4$ SYM theory.
We show that the transfer matrix "building" the fishnet graphs emerges from the
$R-$matrix of non-compact conformal $SU(2,2)$ Heisenberg spin chain with spins
belonging to principal series representations of the four-dimensional conformal
group. We demonstrate explicitly a relationship between this integrable spin
chain and the Quantum Spectral Curve (QSC) of $\mathcal{N}=4$ SYM. Using QSC
and spin chain methods, we construct Baxter equation for $Q-$functions of the
conformal spin chain needed for computation of the anomalous dimensions of
operators of the type $\text{tr}(\phi_1^J)$ where $\phi_1$ is one of the two
scalars of the theory. For $J=3$ we derive from QSC a quantization condition
that fixes the relevant solution of Baxter equation. The scaling dimensions of
the operators only receive contributions from wheel-like graphs. We develop
integrability techniques to compute the divergent part of these graphs and use
it to present the weak coupling expansion of dimensions to very high orders.
Then we apply our exact equations to calculate the anomalous dimensions with
$J=3$ to practically unlimited precision at any coupling. These equations also
describe an infinite tower of local conformal operators all carrying the same
charge $J=3$. The method should be applicable for any $J$ and, in principle, to
any local operators of bi-scalar theory. We show that at strong coupling the
scaling dimensions can be derived from semiclassical quantization of finite gap
solutions describing an integrable system of noncompact $SU(2,2)$ spins. This
bears similarities with the classical strings arising in the strongly coupled
limit of $\mathcal{N}=4$ SYM.

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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin