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<p>We construct a generalisation of the <i>λ</i>-deformation of the Principal Chiral Model (PCM) where we deform just a subgroup <i>F</i> of the full symmetry group <i>G</i>. We find that demanding Lax integrability imposes a crucial restriction, namely that the coset <i>F\G</i> must be symmetric. Surprisingly, we also find that (when <i>F</i> is non-abelian) integrability requires that the term in the action involving only the spectator fields should have a specific <i>λ</i>-dependence, which is a curious modification of the procedure expected from the known <i>F</i> = <i>G</i> 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 <i>λ</i>-deformation. We also explicitly work out the example of <i>G</i> = SU(2) and <i>F</i> = U(1), discussing its renormalisation group flow to two loops.</p>

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Integrability of the λ-deformation of the PCM with spectators

  • 期刊论文

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  • 发表日期：

    2025年3月14日

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  • Riccardo Borsato,
  • Georgios Itsios,
  • J. Luis Miramontes,
  • Konstantinos Siampos

摘要

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\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.