Nested T-Duality

Klimčı́k, Ctirad

doi:10.1007/s11005-006-0084-4

“…These issues can be addressed successfully with a generalization of the well known abelian [5] and non-abelian [6] T-dualities, namely the so-called Poisson-Lie T-duality [7]. Its most notable feature is that it does not rely on the existence of isometries but rather on a rigid group-theoretical structure [7] known as the Drinfeld Double. Nevertheless, it shares some common features with ordinary T-duality.…”

Section: Introductionmentioning

confidence: 99%

“…Pairs of Poisson-Lie T-dual σ-models can be constructed classically from a single duality invariant theory consisting of a WZW model on the Drinfeld Double supplemented with a non-linear interaction term [12]. By choosing a parametrization for a group element of the Double and implementing the constraints that arise as equations of motion, one can eliminate half of the fields and obtain a standard Lorentz invariant σ-model.…”

Section: Introductionmentioning

confidence: 99%

Renormalization of Lorentz non-invariant actions and manifest T-duality

Sfetsos

¹

,

Σιάμπος

²

,

Thompson

³

2010

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We study general two-dimensional sigma-models which do not possess manifest Lorentz invariance. We show how demanding that Lorentz invariance is recovered as an emergent on-shell symmetry constrains these sigma-models. The resulting actions have an underlying group-theoretic structure and resemble Poisson-Lie T-duality invariant actions. We consider the one-loop renormalization of these models and show that the quantum Lorentz anomaly is absent. We calculate the running of the couplings in general and show, with certain non-trivial examples, that this agrees with that of the T-dual models obtained classically from the duality invariant action. Hence, in these cases solving constraints before and after quantization are commuting operations

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“…The conditions in the first and second row are of course standard. Additionally, the condition in the fourth row is also standard and it corresponds to the H-twisted Poisson sigma model [29,30,61]. This table can also be obtained in the context of the AKSZ sigma models and we now show how (see also [28,31] for related discussions).…”

Section: Twisted Dirac Structure Bracketmentioning

confidence: 54%

Sigma models for genuinely non-geometric backgrounds

Jonke¹

2016

Proceedings of Proceedings of the Corfu Summer Institute 2015 — PoS(CORFU2015)

0

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The existence of genuinely non-geometric backgrounds, i.e. ones without geometric dual, is an important question in string theory. In this paper we examine this question from a sigma model perspective. First we construct a particular class of Courant algebroids as protobialgebroids with all types of geometric and non-geometric fluxes. For such structures we apply the mathematical result that any Courant algebroid gives rise to a 3D topological sigma model of the AKSZ type and we discuss the corresponding 2D field theories. It is found that these models are always geometric, even when both 2-form and 2-vector fields are neither vanishing nor inverse of one another. Taking a further step, we suggest an extended class of 3D sigma models, whose world volume is embedded in phase space, which allow for genuinely non-geometric backgrounds. Adopting the doubled formalism such models can be related to double field theory, albeit from a world sheet perspective.1 thanasis@itp.uni-hannover.de 2

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“…The conditions in the first and second row are of course standard. Additionally, the condition in the fourth row is also standard and it corresponds to the H-twisted Poisson sigma model [29,30,61]. This table can also be obtained in the context of the AKSZ sigma models and we now show how (see also [28,31] for related discussions).…”

Section: Bulk/boundary Versus Integrability Conditions For Dirac Strumentioning

confidence: 58%

Sigma models for genuinely non-geometric backgrounds

Chatzistavrakidis

¹

,

Jonke

²

,

Lechtenfeld

³

2015

J. High Energ. Phys.

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The existence of genuinely non-geometric backgrounds, i.e. ones without geometric dual, is an important question in string theory. In this paper we examine this question from a sigma model perspective. First we construct a particular class of Courant algebroids as protobialgebroids with all types of geometric and non-geometric fluxes. For such structures we apply the mathematical result that any Courant algebroid gives rise to a 3D topological sigma model of the AKSZ type and we discuss the corresponding 2D field theories. It is found that these models are always geometric, even when both 2-form and 2-vector fields are neither vanishing nor inverse of one another. Taking a further step, we suggest an extended class of 3D sigma models, whose world volume is embedded in phase space, which allow for genuinely non-geometric backgrounds. Adopting the doubled formalism such models can be related to double field theory, albeit from a world sheet perspective.Comment: 1+34 pages, v2. added references and additional comments; published versio

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Nested T-Duality

Cited by 8 publications

References 19 publications

Renormalization of Lorentz non-invariant actions and manifest T-duality

Renormalization of Lorentz non-invariant actions and manifest T-duality

Sigma models for genuinely non-geometric backgrounds

Sigma models for genuinely non-geometric backgrounds

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