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arXiv · 2407.20323

Integrability of the $\lambda$-deformation of the PCM with spectators

Riccardo Borsato·Georgios Itsios·J. Luis Miramontes·Konstantinos Siampos
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Abstract

We construct a generalisation of the $\lambda$-deformation of the Principal Chiral Model (PCM) where we deform just a subgroup $F$ of the full symmetry group $G$. We find that demanding Lax integrability imposes a crucial restriction, namely that the coset $F\backslash G$ must be symmetric. Surprisingly, we also find that (when $F$ is non-abelian) integrability requires that the term in the action involving only the spectator fields should have a specific $\lambda$-dependence, which is a curious modification of the procedure expected from the known $F=G$ case. The resulting Lax connection has a novel analytical structure, with four single poles as opposed to the two poles of the cases of the PCM and of the standard $\lambda$-deformation. We also explicitly work out the example of $G=SU(2)$ and $F=U(1)$, discussing its renormalisation group flow to two loops.

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Riccardo Borsato, Georgios Itsios, J. Luis Miramontes, Konstantinos Siampos. 2024-07-29. Integrability of the $\lambda$-deformation of the PCM with spectators. https://doi.org/10.1007/jhep03(2025)112

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