The exact C-function in integrable λ-deformed theories

Georgiou, George; Panopoulos, Pantelis; Sagkrioti, Eftychia; Sfetsos, Konstadinos; Σιάμπος, Κωνσταντίνος

doi:10.1016/j.physletb.2018.06.023

Cited by 17 publications

(25 citation statements)

References 48 publications

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“…This is in agreement with the results of [36] to leading order in 1 /k G . In addition, (3.26) is invariant under (3.10) to order 1 /k 2 G , up to a constant…”

Section: C-function and The Anomalous Dimension Of The Current Bilinearsupporting

confidence: 93%

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An exact symmetry in λ-deformed CFTs

Georgiou

Sagkrioti

Sfetsos

et al. 2020

J. High Energ. Phys.

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We consider λ-deformed current algebra CFTs at level k, interpolating between an exact CFT in the UV and a PCM in the IR. By employing gravitational techniques, we derive the two-loop, in the large k expansion, β-function. We find that this is covariant under a remarkable exact symmetry involving the coupling λ, the level k and the adjoint quadratic Casimir of the group. Using this symmetry and CFT techniques, we are able to compute the Zamolodchikov metric, the anomalous dimension of the bilinear operator and the Zamolodchikov C-function at two-loops in the large k expansion, as exact functions of the deformation parameter. Finally, we extend the above results to λ-deformed parafermionic algebra coset CFTs which interpolate between exact coset CFTs in the UV and a symmetric coset space in the IR.

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“…This is in agreement with the results of [36] to leading order in 1 /k G . In addition, (3.26) is invariant under (3.10) to order 1 /k 2 G , up to a constant…”

Section: C-function and The Anomalous Dimension Of The Current Bilinearsupporting

confidence: 93%

“…Next we compute the C-function from Zamolochikov's c-theorem [37] by following the procedure introduce in the present context in [36]. We have that [37] dC dt…”

Section: C-function and The Anomalous Dimension Of The Current Bilinearmentioning

confidence: 99%

An exact symmetry in λ-deformed CFTs

Georgiou

Sagkrioti

Sfetsos

et al. 2020

J. High Energ. Phys.

Self Cite

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show abstract

“…Furthermore, one could exploit the aforementioned non-perturbative symmetries that our models enjoy to compute the anomalous dimensions of current operators, as well as that of primary operators in a similar manner to that in [20-22, 14, 24, 7]. One could also calculate the exact in the deformation parameters C-function of the models presented here as was done in [24] for simpler cases. In that respect the general results in [24] should be a useful starting point.…”

Section: Discussion and Future Directionsmentioning

confidence: 98%

“…2 In addition, anomalous dimensions of current [20] and primary operators [21,22], as well as three-point correlators involving currents and/or primary operators [21,22] were calculated for the models of [6][7][8][9]. Furthermore, the computation of the C-function of Zamolodchikov [23], exactly in the deformation parameter for the case of isotropic perturbations but to leading order in k, was performed in [24] and further generalized for anisotropic λ-deformations in [25].…”

Section: Introductionmentioning

confidence: 99%

The most general λ-deformation of CFTs and integrability

Georgiou

Sfetsos

2019

J. High Energ. Phys.

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We show that the CFT with symmetry group G k 1 × G k 2 × · · · × G k n consisting of WZW models based on the same group G, but at arbitrary integer levels, admits an integrable deformation depending on 2(n − 1) continuous parameters. We derive the all-loop effective action of the deformed theory and prove integrability. We also calculate the exact in the deformation parameters RG flow equations which can be put in a particularly simple compact form. This allows a full determination and classification of the fixed points of the RG flow, in particular those that are IR stable. The models under consideration provide concrete realizations of integrable flows between CFTs. We also consider non-Abelian T-duality type limits.

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“…where we have used the definition θ (m,n) 15) which is analogous to that in (3.4). Note that (3.14) reduces to (2.14) for m = 1, n = 0.…”

Section: The Rg Flow Equationsmentioning

confidence: 99%

Exact results from the geometry of couplings and the effective action

et al. 2019

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We invent a method that exploits the geometry in the space of couplings and the known all-loop effective action, in order to calculate the exact in the couplings anomalous dimensions of composite operators for a wide class of integrable σ-models. These involve both self and mutually interacting current algebra theories. We work out the details for important classes of such operators. In particular, we consider the operators built solely from an arbitrary number of currents of the same chirality, the composite operators which factorize into a chiral and an anti-chiral part, as well as those made up of three currents of mixed chirality. Remarkably enough, the anomalous dimensions of the former two sets of operators turn out to vanish. In our approach, loop computations are completely avoided.

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The exact C-function in integrable λ-deformed theories

Cited by 17 publications

References 48 publications

An exact symmetry in λ-deformed CFTs

An exact symmetry in λ-deformed CFTs

The most general λ-deformation of CFTs and integrability

Exact results from the geometry of couplings and the effective action

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