Non-chiral current algebras for deformed supergroup WZW models

Konechny, Anatoly; Quella, Thomas

doi:10.1007/jhep03(2011)124

Cited by 9 publications

(20 citation statements)

References 34 publications

(100 reference statements)

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“…Note also that in the regularization of [31] no two points, internal or external, can coincide and therefore all δ-functions arising in integrations are set to zero. In contrast in [32] all such δ-functions are kept. The advantage of our regularization is that the symmetry of the correlation functions under k → −k and λ → λ −1 is manifest whereas for the others it is hidden.…”

Section: The Regularization Methods and Useful Integralsmentioning

confidence: 99%

All-loop correlators of integrable λ -deformed σ -models

2016

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We compute the 2-and 3-point functions of currents and primary fields of λ-deformed integrable σ-models characterized also by an integer k. Our results apply for any semisimple group G, for all values of the deformation parameter λ and up to order 1/k. We deduce the OPEs and equal-time commutators of all currents and primaries. We derive the currents' Poisson brackets which assume Rajeev's deformation of the canonical structure of the isotropic PCM, the underlying structure of the integrable λdeformed σ-models. We also present analogous results in two limiting cases of special interest, namely for the non-Abelian T-dual of the PCM and for the pseudodual model.

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Section: The Regularization Methods and Useful Integralsmentioning

confidence: 99%

All-loop correlators of integrable λ -deformed σ -models

2016

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“…Also perturbations of current-current type are explored. It is possible to compute the spectra of perturbed theories [49][50][51], to compute some correlation functions [52,55,56] and to establish Yangian symmetry [53].…”

Section: Discussionmentioning

confidence: 99%

“…If the Killing form of the underlying Lie super algebra vanishes, then current-current perturbations are truly marginal. Further they are under good control and physical quantities can be computed [49][50][51][52][53][54][55][56]. So in principle one can apply the results of these works to the nonlinear A-model.…”

Section: Introductionmentioning

confidence: 99%

Fermionic coset, critical level $ \mathcal{W}_4^{{(2)}} $ -algebra and higher spins

Creutzig

Gao²,

Linshaw³

2012

J. High Energ. Phys.

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The fermionic coset is a limit of the pure spinor formulation of the AdS 5 ×S 5 sigma model as well as a limit of a nonlinear topological A-model, introduced by Berkovits. We study the latter, especially its symmetries, and map them to higher spin algebras.We show the following. The linear A-model possesses affine pgl (4|4) 0 symmetry at critical level and its psl (4|4) 0 current-current perturbation is the nonlinear model. We find that the perturbation preserves W (2) 4 -algebra symmetry at critical level. There is a topological algebra associated to pgl (4|4) 0 with the properties that the perturbation is BRST-exact. Further, the BRST-cohomology contains world-sheet supersymmetric symplectic fermions and the non-trivial generators of the W (2) 4 -algebra. The Zhu functor maps the linear model to a higher spin theory. We analyze its psl (4|4) action and find finite dimensional short multiplets. *

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“…one could search for massive deformations, one can apply it to world-sheet supersymmetric supergroup WZW models [63]. Also our method applies to the current-current deformations recently studied in [28] in this case for the disc as world-sheet. Here it would be interesting to understand how the Yangian symmetry is preserved by current-current perturbations according to the quadratic Casimir for the sphere as world-sheet.…”

Section: Discussionmentioning

confidence: 99%

“…The situation changes when Kac-Moody symmetry ceases to be present. Then perturbative computations starting from the WZW model led to the computation of specific boundary spectra [20,21,22,23] and current correlation functions [24,25,26,27,28]. In both cases the vanishing of the Killing form simplified the perturbative treatment.…”

Section: Introductionmentioning

confidence: 99%

Yangian superalgebras in conformal field theory

Creutzig

2011

Nuclear Physics B

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Quantum Yangian symmetry in several sigma models with supergroup or supercoset as target is established. Starting with a two-dimensional conformal field theory that has current symmetry of a Lie superalgebra with vanishing Killing form we construct non-local charges and compute their properties. Yangian axioms are satisfied, except that the Serre relations only hold for a subsector of the space of fields. Yangian symmetry implies that correlation functions of fields in this sector satisfy Ward identities. We then show that this symmetry is preserved by certain perturbations of the conformal field theory. The main example are sigma models of the supergroups PSL(N|N), OSP(2N+2|2N) and D(2,1;α) away from the WZW point. Further there are the OSP(2N+2|2N) Gross-Neveu models and current-current perturbations of ghost systems, both for the disc as world-sheet. The latter we show to be equivalent to CP N−1|N sigma models, while the former are conjecturally dual to supersphere sigma models. *

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Non-chiral current algebras for deformed supergroup WZW models

Cited by 9 publications

References 34 publications

All-loop correlators of integrable λ -deformed σ -models

All-loop correlators of integrable λ -deformed σ -models

Fermionic coset, critical level $ \mathcal{W}_4^{{(2)}} $ -algebra and higher spins

Yangian superalgebras in conformal field theory

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