The background field method and the non-linear σ-model

Howe, Paul; Papadopoulos, Georgios; Stelle, K.S.

doi:10.1016/0550-3213(88)90379-3

Cited by 123 publications

(141 citation statements)

References 11 publications

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“…(14) it is clear that these translations correspond to multiplying the SU (2) element, G, by a constant, diagonal SU (2) matrix from the left (respectively from the right). Since in the dual variables there is always a translational symmetry and the duality transformation amounts to a canonical transformation (classically) the 'ψ dual' is expected to show the full remaining SU (2) × U (1) symmetry of the original model (15), while for the φ dual only a U (1) × U (1) symmetry is expected.…”

Section: The Deformed Su(2) Principal σ-Model and Some Of Its Dualsmentioning

confidence: 99%

“…The Lagrangian of the deformed σ-model given by Eq. (15) exhibits two obvious Abelian isometries that can be used to construct two different (Abelian) duals: namely the translations in the φ and ψ fields; we call the models obtained this way the 'φ dual' and the 'ψ dual' of the deformed σ model (15). From Eq.…”

Section: The Deformed Su(2) Principal σ-Model and Some Of Its Dualsmentioning

confidence: 99%

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Perturbative quantum (in)equivalence of dual σ models in 2 dimensions

Balog¹,

Forgács²,

Horváth³

et al. 1996

Nuclear Physics B - Proceedings Supplements

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Section: The Deformed Su(2) Principal σ-Model and Some Of Its Dualsmentioning

confidence: 99%

Section: The Deformed Su(2) Principal σ-Model and Some Of Its Dualsmentioning

confidence: 99%

Perturbative quantum (in)equivalence of dual σ models in 2 dimensions

Balog¹,

Forgács²,

Horváth³

et al. 1996

Nuclear Physics B - Proceedings Supplements

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show abstract

“…To examine the anomalies for (2,0)-supersymmetric sigma models with Nijenhuis symmetries, we quantise the theory in the background field method. As in the case of (2,0)-supersymmetric sigma models with target spaces complex manifolds, the model can be quantised in such a way that the background/quantum field split symmetry [14], (1,0) supersymmetry and sigma model manifold reparameterisations are manifestly preserved quantum mechanically. The arguments for this are similar to those of ref.…”

Section: Anomaliesmentioning

confidence: 99%

“…The currents of the theory are 14) where the components of the G 0 += , G 0 −= are the energy momentum tensor and the (1,0) and (0,1) supersymmetry currents, the components of G 1 ++ and G 1 −− are the (2,0) and (0,2) supersymmetry currents and two U(1) currents, and the components of P += and P −= are the currents corresponding to Nijenhuis symmetries. All the above currents are conserved, i.e.…”

Section: The Poisson Bracket Algebra Of Chargesmentioning

confidence: 99%

(2,0)-supersymmetric sigma models and almost complex structures

Papadopoulos

1995

Nuclear Physics B

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We find a new class of (2,0)-supersymmetric two-dimensional sigma models with torsion and target spaces almost complex manifolds extending similar results for models with (2,2) supersymmetry. These models are invariant under a new symmetry which is generated by a Noether charge of Lorentz weight one and it is associated to the Nijenhuis tensor of the almost complex structure of the sigma model target manifold. We compute the Poisson bracket algebra of charges of the above (2,0)-and (2,2)-supersymmetric sigma models and show that it closes but it is not isomorphic to the standard (2,0) and (2,2) supersymmetry algebra, respectively. Examples of such (2,0)-and (2,2)-supersymmetric sigma models with target spaces group manifolds are also given. In addition, we study the quantisation of the (2,0)-supersymmetric sigma models, compute the anomalies of their classical symmetries and examine their cancellation. Furthermore, we examine the massive extension of (2,0)-supersymmetric sigma models with target spaces almost complex manifolds, and study the topological twist of the new supersymmetry algebras.

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“…Therefore it is surprising that the counterterms of the sigma model with affine-metric manifold differ from counter terms of the sigma model with Riemannian manifold [6]. This difference can not be reduced to the metric redefenition caused by infinitesimal coordinate transformation [2] or to the nonlinear renormalization of the quantum fields [8]. In the paper [6], the counter terms are calculated for conventional sigma model without assuming a metric connection for the geodesic line equation in covariant background field method.…”

Section: Introductionmentioning

confidence: 99%

Bosonic string in affine-metric curved space

Tarasov

1994

Physics Letters B

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The sigma model approach to the closed bosonic string on the affine-metric manifold is considered. The two-loop metric counterterms for the nonlinear twodimensional sigma model with affine-metric target manifold are calculated. The correlation of the metric and affine connection is considered as the result of the conformal invariance condition for the nonlinear sigma model. The examples of the nonflat nonRiemannian manifolds resulting in the trivial metric beta-function are suggested.

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The background field method and the non-linear σ-model

Cited by 123 publications

References 11 publications

Perturbative quantum (in)equivalence of dual σ models in 2 dimensions

Perturbative quantum (in)equivalence of dual σ models in 2 dimensions

(2,0)-supersymmetric sigma models and almost complex structures

Bosonic string in affine-metric curved space

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