Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sigma models with local couplings: a new integrability -- RG flow
  connection   We consider several classes of $\sigma$-models (on groups and symmetric
spaces, $\eta$-models, $\lambda$-models) with local couplings that may depend
on the 2d coordinates, e.g. on time $\tau$. We observe that (i) starting with a
classically integrable 2d $\sigma$-model, (ii) formally promoting its couplings
$h_\alpha$ to functions $h_\alpha(\tau)$ of 2d time, and (iii) demanding that
the resulting time-dependent model also admits a Lax connection implies that
$h_\alpha(\tau)$ must solve the 1-loop RG equations of the original theory with
$\tau$ interpreted as RG time. This provides a novel example of an
'integrability - RG flow' connection. The existence of a Lax connection
suggests that these time-dependent $\sigma$-models may themselves be understood
as integrable. We investigate this question by studying the possibility of
constructing non-local and local conserved charges. Such $\sigma$-models with
$D$-dimensional target space and time-dependent couplings subject to the RG
flow naturally appear in string theory upon fixing the light-cone gauge in a
$(D+2)$-dimensional conformal $\sigma$-model with a metric admitting a
covariantly constant null Killing vector and a dilaton linear in the null
coordinate.

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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys