Classifying integrable symmetric space strings via factorized scattering

Wulff, Linus

doi:10.1007/jhep02(2018)106

Cited by 16 publications

(30 citation statements)

References 73 publications

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“…The next simplest amplitude to consider is x 5 x 6 → x 7 x 8 ϕϕ. We will now show that the vanishing of this, and similar, amplitudes leads to the same conditions derived in [21,33] from vanishing of the massless particle production amplitudes discussed above.…”

Section: Symmetric Spaces With Nsns Fluxsupporting

confidence: 57%

“…In [21,33] the absence of particle production in certain massless GKP scattering amplitudes was used as a criterion for integrability. Since the scattering of massless particles does not in general factorize even in an integrable theory one can question using such a condition to rule out integrability [25].…”

Section: Symmetric Spaces With Nsns Fluxmentioning

confidence: 99%

“…Let us recall the argument of [21,33]. Looking at the amplitude for x 5 x 6 → x 7 x 7 x 9 , where x 5,6 and x 7,8 belong to different factors in the geometry, one sees from the Lagrangian (3.3) and (3.4) that, in the low-energy limit, the only relevant interaction terms are the ones coming from the B-field, so that the only contribution to the amplitude comes from the Feynman diagram…”

Section: Symmetric Spaces With Nsns Fluxmentioning

confidence: 99%

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Constraining integrable AdS/CFT with factorized scattering

Wulff

2019

J. High Energ. Phys.

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We consider (warped) AdS string backgrounds which allow for a GKP spinning string/null cusp solution. Integrability implies that the worldsheet S-matrix should factorize, which in turn constrains the form of the warp factor as a function of the coordinates of the internal space. This constraint is argued to rule out integrability for all supersymmetric AdS 7 and AdS 6 backgrounds as well as AdS 5 Gaiotto-Maldacena backgrounds and a few highly supersymmetric AdS 4 and AdS 3 backgrounds.

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Section: Symmetric Spaces With Nsns Fluxsupporting

confidence: 57%

Section: Symmetric Spaces With Nsns Fluxmentioning

confidence: 99%

Section: Symmetric Spaces With Nsns Fluxmentioning

confidence: 99%

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Constraining integrable AdS/CFT with factorized scattering

Wulff

2019

J. High Energ. Phys.

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“…Examples of integrable 2d models are few and hard to find. In the context of string theory, one is interested in finding new classically integrable 2d σ-models (see, e.g., [1] and refs. there).…”

Section: Introductionmentioning

confidence: 99%

On the massless tree-level S-matrix in 2d sigma models

Hoare¹,

Levine²,

Tseytlin³

2019

J. Phys. A: Math. Theor.

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Motivated by the search for new integrable string models, we study the properties of massless tree-level S-matrices for 2d σ-models expanded near the trivial vacuum. We find that, in contrast to the standard massive case, there is no apparent link between massless S-matrices and integrability: in well-known integrable models the tree-level massless S-matrix fails to factorize and exhibits particle production. Such tree-level particle production is found in several classically integrable models: the principal chiral model, its classically equivalent "pseudo-dual" model, its non-abelian dual model and also the SO(N +1)/SO(N ) coset model. The connection to integrability may, in principle, be restored if one expands near a nontrivial vacuum with massive excitations. We discuss IR ambiguities in 2d massless tree-level amplitudes and their resolution using either a small mass parameter or the i -regularization. In general, these ambiguities can lead to anomalies in the equivalence of the S-matrix under field redefinitions, and may be linked to the observed particle production in integrable models. We also comment on the transformation of massless S-matrices under σ-model T-duality, comparing the standard and the "doubled" formulations (with T-duality covariance built into the latter). 1 bhoare@ethz.ch 2 n.

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“…The classification of classically integrable backgrounds was performed in[47]. See also[48][49][50] for discussions on…”

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confidence: 99%

An index for quantum integrability

2019

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The existence of higher-spin quantum conserved currents in two dimensions guarantees quantum integrability. We revisit the question [1] of whether classically-conserved local higher-spin currents in two-dimensional sigma models survive quantization. We define an integrability index IpJq for each spin J, with the property that IpJq is a lower bound on the number of quantum conserved currents of spin J. In particular, a positive value for the index establishes the existence of quantum conserved currents. For a general coset model, with or without extra discrete symmetries, we derive an explicit formula for a generating function that encodes the indices for all spins. We apply our techniques to the CP N´1 model, the OpN q model, and the flag sigma model U pN q U p1q N . For the OpN q model, we establish the existence of a spin-6 quantum conserved current, in addition to the well-known spin-4 current. The indices for the CP N´1 model for N ą 2 are all non-positive, consistent with the fact that these models are not integrable. The indices for the flag sigma model U pN q U p1q N for N ą 2 are all negative. Thus, it is unlikely that the flag sigma models are integrable.

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Classifying integrable symmetric space strings via factorized scattering

Cited by 16 publications

References 73 publications

Constraining integrable AdS/CFT with factorized scattering

Constraining integrable AdS/CFT with factorized scattering

On the massless tree-level S-matrix in 2d sigma models

An index for quantum integrability

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