Target space duality I: general theory

Alvarez, Orlando

doi:10.1016/s0550-3213(00)00314-x

Cited by 25 publications

(36 citation statements)

References 32 publications

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“…(2). It doesn't really make sense as a cohomology class or differential form since the nonclassical T-dual is not a space; rather, it is subsumed in the noncommutative structure of the dual.…”

Section: 4mentioning

confidence: 99%

T-Duality for Torus Bundles with H-Fluxes via Noncommutative Topology

Mathai

Rosenberg

2004

Commun. Math. Phys.

141

326

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Abstract. It is known that the T-dual of a circle bundle with H-flux (given by a Neveu-Schwarz 3-form) is the T-dual circle bundle with dual H-flux. However, it is also known that torus bundles with H-flux do not necessarily have a T-dual which is a torus bundle. A big puzzle has been to explain these mysterious "missing T-duals." Here we show that this problem is resolved using noncommutative topology. It turns out that every principal T 2 -bundle with H-flux does indeed have a T-dual, but in the missing cases (which we characterize), the T-dual is non-classical and is a bundle of noncommutative tori. The duality comes with an isomorphism of twisted K-theories, just as in the classical case. The isomorphism of twisted cohomology which one gets in the classical case is replaced by an isomorphism of twisted cyclic homology.

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Section: 4mentioning

confidence: 99%

T-Duality for Torus Bundles with H-Fluxes via Noncommutative Topology

Mathai

Rosenberg

2004

Commun. Math. Phys.

141

326

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“…The sigma model with target space M, metric g and 2-form B will be denoted by (M, g, B) and has lagrangian Our default scenario is general riemannian manifolds but we often specialize to the case of Lie groups. Overall, the methods we use are differential geometric ones that expand on ideas in [1,10,11]. The bundle of orthonormal frames, the Cartan structural equations and the exterior differential calculus play a central role.…”

Section: Introductionmentioning

confidence: 99%

Pseudoduality in sigma models

Alvarez¹

2002

Nuclear Physics B

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We revisit classical "on shell" duality, i.e., pseudoduality, in two dimensional conformally invariant classical sigma models and find some new interesting results. We show that any two sigma models that are "on shell" duals have opposite 1-loop renormalization group beta functions because of the integrability conditions for the pseudoduality transformation. A new result states for any two compact Lie groups of the same dimension there is a natural pseudoduality transformation that maps classical solutions of the WZW model on the first group into solutions of the WZW model on the second group. This transformation preserves the stress-energy tensor. The two groups can be non-isomorphic such as B l and C l in the Cartan notation. This transformation can be used for a new construction of non-local conserved currents. The new non-local currents on G depend on the choice of dual group G.

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“…As in [28] it is convenient to choose an orthonormal frame {ω i } with the antisymmetric riemannian connection ω ij . The Cartan structural equations are…”

Section: Introductionmentioning

confidence: 99%

“…The orthogonal matrix valued functions T ± : M × M → SO(n) are not arbitrary but related by 11) where the antisymmetric tensor n ij on M × M satisfies some PDEs given in [28]. In this article we relax such restrictions on T ± and consider orthogonal matrix valued functions T ± : Σ → SO(n) with the constraint that solutions to the the sigma model (M, g, B) are mapped into solutions of ( M,g, B) and vice versa.…”

Section: Introductionmentioning

confidence: 99%

Target space pseudoduality between dual symmetric spaces

Alvarez

2000

Nuclear Physics B

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A set of on shell duality equations is proposed that leads to a map between strings moving on symmetric spaces with opposite curvatures. The transformation maps "waves" on a riemannian symmetric space M to "waves" on its dual riemannian symmetric space M . This transformation preserves the energy momentum tensor though it is not a canonical transformation. The preservation of the energy momentum tensor has a natural geometrical interpretation. The transformation maps "particle-like solutions" into static "soliton-like solutions". The results presented here generalize earlier results of E. Ivanov.

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Target space duality I: general theory

Cited by 25 publications

References 32 publications

T-Duality for Torus Bundles with H-Fluxes via Noncommutative Topology

T-Duality for Torus Bundles with H-Fluxes via Noncommutative Topology

Pseudoduality in sigma models

Target space pseudoduality between dual symmetric spaces

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