Renormalization group limit cycles and field theories for elliptic<i>S</i>-matrices

LeClair, André; Sierra, Germȧn

doi:10.1088/1742-5468/2004/08/p08004

Cited by 14 publications

(29 citation statements)

References 40 publications

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“…and cyclic permutations in 1, 2, 3. Then plugging these into (7.7) we find (6.2), a result consistent with that in [12] (after relabeling and rescaling).…”

Section: The Su(2) Casesupporting

confidence: 77%

“…For the case of SU(2) consider turning on just three couplings, h A , A = 1, 2, 3 a case that has been considered in [12]. Referring to (7.1) and choosing as the non-vanishing…”

Section: The Su(2) Casementioning

confidence: 99%

“…The initial aim of this work was to compute the RG flows for the anisotropic G = SU(2) case, with diagonal coupling matrix λ ab and then to compare the results with the analogue ones in [12] which were found using [7]. Nevertheless, we managed to compute the RG flow equations for the most general class of the σ-models of [8] containing a general deformation matrix λ ab and for general simple group G, and present the result in a remarkably simple and compact form.…”

Section: Introductionmentioning

confidence: 99%

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Gauged WZW-type theories and the all-loop anisotropic non-Abelian Thirring model

Sfetsos

Σιάμπος

2014

Nuclear Physics B

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We study what we call the all-loop anisotropic bosonized Thirring σ-model. This interpolates between the WZW model and the non-Abelian T-dual of the principal chiral model for a simple group. It has an invariance involving the inversion of the matrix parametrizing the coupling constants. We compute the general renormalization group flow equations which assume a remarkably simple form and derive its properties. For symmetric couplings, they consistently truncate to previous results in the literature. One of the examples we provide gives rise to a first order system of differential equations interpolating between the Lagrange and the Darboux-Halphen integrable systems.

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“…and cyclic permutations in 1, 2, 3. Then plugging these into (7.7) we find (6.2), a result consistent with that in [12] (after relabeling and rescaling).…”

Section: The Su(2) Casesupporting

confidence: 77%

“…For the case of SU(2) consider turning on just three couplings, h A , A = 1, 2, 3 a case that has been considered in [12]. Referring to (7.1) and choosing as the non-vanishing…”

Section: The Su(2) Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Gauged WZW-type theories and the all-loop anisotropic non-Abelian Thirring model

Sfetsos

Σιάμπος

2014

Nuclear Physics B

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“…So either the sigma model limit itself is more subtle in this regime, or the lambda model is not consistently regularized as a spin chain. However, the situation in the λ < ξ regime lends weight to the idea that theories with a cyclic RG flow do not admit a continuum limit [124].…”

Section: Discussionmentioning

confidence: 99%

Quantum anisotropic sigma and lambda models as spin chains

Appadu¹,

Hollowood²,

Price³

et al. 2018

J. Phys. A: Math. Theor.

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We consider lambda and anisotropic deformations of the SU(2) principal chiral model and show how they can be quantized in the Hamiltonian formalism on a lattice as a suitable spin chain. The spin chain is related to the higher spin XXZ Heisenberg chain and can be solved by using the Bethe Ansatz. This yields the spectrum and S-matrix of the excitations. In particular, we find the S-matrix in the gapped anti-ferromagnetic regime. In this regime, a continuum limit does not exist and this suggests that the field theories in this regime, precisely ones with a cyclic RG like the Yang-Baxter deformations, may only exist as effective theories. In a certain limit, we show that the XXZ type lambda model gives the symmetric space SU(2)/U(1) lambda model and, hence, we are able to find its spectrum and S-matrix and show that it gives the S-matrix of the O(3) sigma model in the appropriate limit. Finally, we show the full consistency of the S-matrix and the Lagrangian formulations of the lambda model, by coupling to a conserved charge and computing the way the ground state energy changes in both pictures.

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“…anisotropic XXZ theories in the regime β > α, precisely the models with affine quantum group symmetry with a real q, have an exotic cyclic type RG behaviour. The interpretation of this is quite subtle but has been considered in the closely related context of perturbed WZW models in [51][52][53].…”

Section: Modelmentioning

confidence: 99%

Yang Baxter and anisotropic sigma and lambda models, cyclic RG and exact S-matrices

Appadu

Hollowood

Price

et al. 2017

J. High Energ. Phys.

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Integrable deformation of SU(2) sigma and lambda models are considered at the classical and quantum levels. These are the Yang-Baxter and XXZ-type anisotropic deformations. The XXZ type deformations are UV safe in one regime, while in another regime, like the Yang-Baxter deformations, they exhibit cyclic RG behaviour. The associated affine quantum group symmetry, realized classically at the Poisson bracket level, has q a complex phase in the UV safe regime and q real in the cyclic RG regime, where q is an RG invariant. Based on the symmetries and RG flow we propose exact factorizable S-matrices to describe the scattering of states in the lambda models, from which the sigma models follow by taking a limit and non-abelian T-duality. In the cyclic RG regimes, the S-matrices are periodic functions of rapidity, at large rapidity, and in the Yang-Baxter case violate parity.

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Renormalization group limit cycles and field theories for ellipticS-matrices

Cited by 14 publications

References 40 publications

Gauged WZW-type theories and the all-loop anisotropic non-Abelian Thirring model

Gauged WZW-type theories and the all-loop anisotropic non-Abelian Thirring model

Quantum anisotropic sigma and lambda models as spin chains

Yang Baxter and anisotropic sigma and lambda models, cyclic RG and exact S-matrices

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