Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrability vs. RG flow in $G \times G$ and $G \times G /H$ sigma
  models   We consider a class of 2d $\sigma$-models on products of group spaces that
provide new examples of a close connection between integrability and stability
under the RG flow. We first study the integrable $G \times G$ model derived
from the affine Gaudin construction (for which the 1-loop $\beta$-functions
were found in arXiv:2010.07879) and show that its condition of integrability is
preserved also by the 2-loop RG flow. We then investigate the RG flow in the
gauged $G \times G /H$ model, in particular the integrable $T^{1,1}$ model
found in arXiv:2010.05573. We also construct a new class of integrable $G
\times G /H$ models in the case when the subgroup $H$ is abelian. In the
simplest case of $G=SU_2$, $H=U_1$ this leads to an integrable $\sigma$-model
on the $T^{1,q}$ space (with a particular $B$-field). This model is also shown
to be stable under the 2-loop RG flow, and we relate this property to its
invariance under T-duality in an isometric $U_1$ direction. This $T^{1,q}$
model may be interpreted as an integrable deformation of the GMM model (of two
coupled WZW theories with generic levels) away from the conformal point.

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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: math