Integrability of the λ-deformation of the PCM with spectators

A bstract 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.