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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.20323 |
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| _version_ | 1866910889092841472 |
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| author | Borsato, Riccardo Itsios, Georgios Miramontes, J. Luis Siampos, Konstantinos |
| author_facet | Borsato, Riccardo Itsios, Georgios Miramontes, J. Luis Siampos, Konstantinos |
| contents | We construct a generalisation of the $λ$-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 $λ$-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 $λ$-deformation. We also explicitly work out the example of $G=SU(2)$ and $F=U(1)$, discussing its renormalisation group flow to two loops. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20323 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integrability of the $λ$-deformation of the PCM with spectators Borsato, Riccardo Itsios, Georgios Miramontes, J. Luis Siampos, Konstantinos High Energy Physics - Theory We construct a generalisation of the $λ$-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 $λ$-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 $λ$-deformation. We also explicitly work out the example of $G=SU(2)$ and $F=U(1)$, discussing its renormalisation group flow to two loops. |
| title | Integrability of the $λ$-deformation of the PCM with spectators |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2407.20323 |