On non-abelian duality

Álvarez, Enrique; Álvarez‐Gaumé, Luis; Lozano, Yolanda

doi:10.1016/0550-3213(94)90093-0

Cited by 206 publications

(302 citation statements)

References 39 publications

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“…The results of [28] suggest that T-duality should generalise to this case, but the non-abelian structure leads to issues similar to those that arise in non-abelian duality [36], [37], [38], so that the approach used here appears difficult to implement in that case.…”

Section: T-folds and T-dualitymentioning

confidence: 95%

Global aspects of T-duality, gauged sigma models and T-folds

Hull

2007

J. High Energy Phys.

116

205

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The gauged sigma-model argument that string backgrounds related by T-dual give equivalent quantum theories is revisited, taking careful account of global considerations. The topological obstructions to gauging sigma-models give rise to obstructions to Tduality, but these are milder than those for gauging: it is possible to T-dualise a large class of sigma-models that cannot be gauged. For backgrounds that are torus fibrations, it is expected that T-duality can be applied fibrewise in the general case in which there are no globally-defined Killing vector fields, so that there is no isometry symmetry that can be gauged; the derivation of T-duality is extended to this case. The T-duality transformations are presented in terms of globally-defined quantities. The generalisation to non-geometric string backgrounds is discussed, the conditions for the T-dual background to be geometric found and the topology of T-folds analysed.

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Section: T-folds and T-dualitymentioning

confidence: 95%

Global aspects of T-duality, gauged sigma models and T-folds

Hull

2007

J. High Energy Phys.

116

205

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“…The preservation of Weyl invariance under non-abelian duality [55,56] and Poisson-Lie duality [50,51,57] has been discussed extensively in the literature. In such expositions a Weyl anomaly is typically associated to integrating out the degrees of freedom corresponding to a non-unimodular algebra, that is whose structure constants satisfy f ab b = 0.…”

Section: Discussionmentioning

confidence: 99%

Poisson-Lie duals of the η deformed symmetric space sigma model

Hoare

Seibold

2017

J. High Energ. Phys.

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Poisson-Lie dualising the η deformation of the G/H symmetric space sigma model with respect to the simple Lie group G is conjectured to give an analytic continuation of the associated λ deformed model. In this paper we investigate when the η deformed model can be dualised with respect to a subgroup G 0 of G. Starting from the first-order action on the complexified group and integrating out the degrees of freedom associated to different subalgebras, we find it is possible to dualise when G 0 is associated to a subDynkin diagram. Additional U 1 factors built from the remaining Cartan generators can also be included. The resulting construction unifies both the Poisson-Lie dual with respect to G and the complete abelian dual of the η deformation in a single framework, with the integrated algebras unimodular in both cases. We speculate that extending these results to the path integral formalism may provide an explanation for why the η deformed AdS 5 × S 5 superstring is not one-loop Weyl invariant, that is the couplings do not solve the equations of type IIB supergravity, yet its complete abelian dual and the λ deformed model are.

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“…If the non-abelian group G is non-compact, there may be an anomaly that prevents the dual model from being conformal. An example of this type was considered in [34] and the understanding of the anomaly was found in [35]. In this paper it is also realized that a better treatment of non-abelian duality is to express the dual theory in terms of a group-valued coordinate g instead of the algebravalued coordinate Λ, this can be achieved by performing a non-local change of variables ∂Λ → g −1 ∂g.…”

Section: Non-abelian T -Dualitymentioning

confidence: 99%

“…Consider the σ-model action (1) and assume that the target space metric has a group G of non-abelian isometries [10], [33], [34], [35]. In this case, Q MN does depend on X m and transforms accordingly under X m → g m n X n , g ∈ G. We gauge the symmetry corresponding to a subgroup…”

Section: Non-abelian T -Dualitymentioning

confidence: 99%

Duality and global symmetries

Quevedo

1998

Nuclear Physics B - Proceedings Supplements

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Duality symmetries are reviewed. A sufficient condition for duality is the existence of a global symmetry. This can be used as a guideline to systematically prove duality between different field theories. Bosonization and T -duality, for abelian and non-abelian global symmetries, are discussed in detail as well as duality for general antisymmetric tensor field theories. In this case, the presence of topological defects break the global symmetry but duality survives manifesting itself in a different way. Open questions and current limitations of this approach to prove all known dualities are discussed.To the hundreds of thousands of Guatemalan citizens who sacrificed their lives during more than three decades of civil war, especially to those I had the privilege to know and love, and who I now miss.

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On non-abelian duality

Cited by 206 publications

References 39 publications

Global aspects of T-duality, gauged sigma models and T-folds

Global aspects of T-duality, gauged sigma models and T-folds

Poisson-Lie duals of the η deformed symmetric space sigma model

Duality and global symmetries

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