An exact symmetry in λ-deformed CFTs

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We continue our study of λ-deformed σ-models by setting up a 1 k perturbative expansion around the free field point for cosets, in particular for the λ-deformed SU(2)/U(1) coset CFT. We construct an interacting field theory in which all deformation effects are manifestly encoded in the interaction vertices. Using this we reproduce the known βfunction and the anomalous dimension of the composite operator perturbing away from the conformal point. We introduce the λ-dressed parafermions which have an essential Wilsonlike phase in their expressions. Subsequently, we compute their anomalous dimension, as well as their four-point functions, as exact functions of the deformation and to leading order in the k expansion. Correlation functions with an odd number of these parafermions vanish as in the conformal case.

Section: Jhep07(2020)187supporting

confidence: 92%

“…This expression is in perfect agreement with equation (4.16) of [28], where the anomalous dimension of the perturbing operator was found by using the geometry in the space JHEP07(2020)187…”

Section: Jhep07(2020)187supporting

confidence: 87%

Section: Discussion and Future Directionsmentioning

confidence: 75%

“…28) for some coefficients c i and a basis of operators with engineering dimension (1, 1) O i 4. However, notice that the overlap of the leading and subleading term in (4.28) is zero.…”

mentioning

confidence: 99%

See 2 more Smart Citations

A free field perspective of λ-deformed coset CFT’s

Georgiou

Sfetsos

Σιάμπος

2020

Self Cite

“…It would be interesting to investigate what equation replaces (1.2) for these models, if any. In addition, it would be also interesting to extend our analysis for the two-parameter integrable deformation of the coset CFT SU(2) k × SU(2) k /U(1) [30], explicitly constructed in [41], whose one-loop renormalization group flows were computed in [42]. Finally, it would also be interesting to study the renormalization of the integrable coset models recently constructed in [43].…”

Section: Jhep02(2021)065mentioning

confidence: 98%

RG flows of integrable σ-models and the twist function

Delduc

Lacroix

Sfetsos

et al. 2021

Self Cite

In the study of integrable non-linear σ-models which are assemblies and/or deformations of principal chiral models and/or WZW models, a rational function called the twist function plays a central rôle. For a large class of such models, we show that they are one-loop renormalizable, and that the renormalization group flow equations can be written directly in terms of the twist function in a remarkably simple way. The resulting equation appears to have a universal character when the integrable model is characterized by a twist function.

New integrable coset sigma models

Arutyunov

Bassi

Lacroix

2021

By using the general framework of affine Gaudin models, we construct a new class of integrable sigma models. They are defined on a coset of the direct product of N copies of a Lie group over some diagonal subgroup and they depend on 3N − 2 free parameters. For N = 1 the corresponding model coincides with the well-known symmetric space sigma model. Starting from the Hamiltonian formulation, we derive the Lagrangian for the N = 2 case and show that it admits a remarkably simple form in terms of the classical ℛ-matrix underlying the integrability of these models. We conjecture that a similar form of the Lagrangian holds for arbitrary N. Specifying our general construction to the case of SU(2) and N = 2, and eliminating one of the parameters, we find a new three-parametric integrable model with the manifold T1,1 as its target space. We further comment on the connection of our results with those existing in the literature.