Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: Poisson-Lie T-duality

Bottom of Page

1 to 26 of 26

  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMar 13th 2018

    started a bare minimum at Poisson-Lie T-duality, for the moment just so as to have a place to record the two original references

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeApr 12th 2018
    • (edited Apr 12th 2018)

    added more references, in particular Ossa-Quevedo 92, which is maybe the first one.

    Made “nonabelian T-duality” a redirect

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeApr 12th 2018

    Are you looking at this with regard to Higher T-duality? Any interest in higher non-abelian T-duality for, say, String(G)String(G)?

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 12th 2018
    • (edited Apr 12th 2018)

    Yes and no: The question in the background was whether the “geometric” complement of “topological” 3-spherical T-duality could be Poisson-Lie T-duality for isometry group SU(2)SU(2). I still don’t know on the math side. But at least the physics contexts do not match: The Poisson-Lie T-duality is based on string sigma-models, while the realization of spherical T-duality that we found replaces strings by 5-branes.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 7th 2018
    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeAug 16th 2018

    added pointer to

    • Branislav Jurco, Jan Vysoky, Poisson-Lie T-duality of String Effective Actions: A New Approach to the Dilaton Puzzle, Journal of Geometry and Physics Volume 130, August 2018, Pages 1-26 (arXiv:1708.04079)

    diff, v5, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeOct 24th 2018

    added pointer to yesterday’s

    diff, v6, current

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJan 9th 2019

    added the following warning, based on discussion we had at the meeting String and M-theory, Singapre 2018. I am not aware of any written reference that would make this statement, but if anyone has one, it should be added.

    It has been proven that these generalized T-dualities are are/induce equivalences of the corresponding string sigma-models at the level of classical field theory. However it seems to be open, and in fact questionable, that away from standard T-duality this yields an equivalence at the level of worldsheet quantum field theories, hence it is open whether Poisson-Lie/non-abelian T-duality is really a duality operation on perturbative string theory vacua.

    diff, v7, current

  9. Added the reference to Double Field Theory on group manifolds

    Anonymous

    diff, v8, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJan 14th 2019

    Thanks! I moved your paragraph from the References-section to the main text, and have it cite your reference there.

    diff, v9, current

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJan 15th 2019

    added pointer to today’s discussion of nonabelian T-folds in

    diff, v10, current

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeFeb 14th 2019
    • (edited Feb 14th 2019)

    My contact person gave me the following more detailed assessment of the non-duality status of non-abelian T-duality by email. For the moment I have no citations for this, apart from this private correspondence, but since it seems to be very worthwhile information, I have put it into the entry, like so:

    While ordinary abelian T-duality is supposedly a full duality in string theory, in particular in that it is an equivalence on the string perturbation series to all orders of the string length/Regge slope α′\alpha' and the string coupling constant g sg_s, it has apparntly been shown by Martin Roček (citation?) that there are topological obstructions at higher genus for non-abelian T-duality, letting it break down in higher orders of g sg_s; and already a genus-0 (tree level) it apparently breaks down for the open string (i.e. on punctured disks) at some order of α′\alpha'.

    If any expert sees this, please feel invited to correct/expand.

    diff, v11, current

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeSep 16th 2019

    Added pointer to today’s

    diff, v13, current

    • CommentRowNumber14.
    • CommentAuthorLuigi
    • CommentTimeSep 19th 2019

    Does this new duality reduce to higher T-duality in the abelian case? At first sight it looks like the dual algebra being shifted h′=h *[n−2]h' = h^\ast[n-2] does not allow it

    • CommentRowNumber15.
    • CommentAuthorUrs
    • CommentTimeSep 20th 2019

    It would be interesting to find a relation, but in the present form I’d think neither can reduce to the other, simply because they formulate different aspects of T-duality:

    Here the Poisson-Lie perspective focuses on the local geometric content, while the higher T-duality we described is the higher generalization of topological T-duality, albeit rationalized.

    To see how the two higher generalizations relate to each other, it would hence be useful to first have a concrete relation between ordinary Poisson-Lie T-duality and ordinary topological T-duality. Did anyone look into that?

    Another vague thought one might have here is that, due to S 3≃SU(2)S^3 \simeq SU(2), the higher 3-spherical topological T-duality is somehow related to non-higher but 𝔰𝔲(2)\mathfrak{su}(2)-nonabelian T-duality. But beyond the coincidental S 3≃SU(2)S^3 \simeq SU(2) there may be no real hint for this, and in fact the physics pictures behind the two sides are disparate (M5-brane physics on one hand, perturbative string sigma models on the other.)

    So in summary, I don’t know. And I am not thinking about it. But it seems like something worth exploring.

    • CommentRowNumber16.
    • CommentAuthorUrs
    • CommentTimeOct 21st 2019

    added pointer to:

    • Ladislav Hlavatý, Ivo Petr, Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity Equations (arxiv:1910.08436)

    diff, v14, current

    • CommentRowNumber17.
    • CommentAuthorUrs
    • CommentTimeNov 19th 2019

    added pointer to today’s

    • Emanuel Malek, Daniel C. Thompson, Energy Physics - Theory Poisson-Lie U-duality in Exceptional Field Theory (arxiv:1911.07833)

    diff, v15, current

    • CommentRowNumber18.
    • CommentAuthorUrs
    • CommentTimeDec 17th 2019
    • (edited Dec 17th 2019)

    added pointer to today’s

    discussion of non-abelian T-duality from a comprehensive picture of higher differential geometry, relating Kaluza-Klein compactification on principal ∞-bundles to double field theory, T-folds, type II geometry, exceptional geometry, etc.:

    diff, v17, current

    • CommentRowNumber19.
    • CommentAuthorUrs
    • CommentTimeApr 21st 2020

    added pointer to today’s

    diff, v19, current

    • CommentRowNumber20.
    • CommentAuthorUrs
    • CommentTimeApr 28th 2020

    added pointer to today’s

    • Francesco Bascone, Franco Pezzella, Patrizia Vitale, Poisson-Lie T-Duality of WZW Model via Current Algebra Deformation (arXiv:2004.12858)

    diff, v22, current

    • CommentRowNumber21.
    • CommentAuthorLuigi
    • CommentTimeJun 23rd 2020

    Added a pointer to today

    • Chris D. A. Blair, Daniel C. Thompson, Sofia Zhidkova, Exploring Exceptional Drinfeld Geometries (arxiv:2006.12452)

    diff, v23, current

    • CommentRowNumber22.
    • CommentAuthorLuigi
    • CommentTimeJun 23rd 2020
    • (edited Jun 23rd 2020)

    I was also thinking something about this.

    They limited themselves to “Exceptional Drinfel’d doubles” representable by TD≃TG⊕∧ 2T *GT D \simeq T G \oplus \wedge^2T^\ast G for some subgroup GG, in analogy with what happens for classical Drinfel’d doubles (i.e. TD≃TG⊕T *GT D\simeq T G \oplus T^\ast G).

    Now, as far as I understand the Drinfel’d double D(G)D(G) of a group GG is related to a cocycle ω∈H 3(G,ℤ)\omega\in H^3(G,\mathbb{Z}) (in particular, a flat gerbe(?)).

    It looks to me that they are trying to define something analogous by using ω∈H 4(G,ℤ)\omega\in H^4(G,\mathbb{Z}).

    Maybe then a full working definition of an “Exceptional Drinfel’d double” would require a to be in correspondence an element of the cohomotopy π 4(G)\pi^4(G), in the spirit of Exceptional geometry as given by differential cohomotopy theory.

    • CommentRowNumber23.
    • CommentAuthorUrs
    • CommentTimeJul 17th 2020

    added pointer to today’s

    diff, v24, current

    • CommentRowNumber24.
    • CommentAuthorUrs
    • CommentTimeNov 16th 2021

    added pointer to today’s

    • Ali Eghbali, Reza Naderi, Adel Rezaei-Aghdam, Non-Abelian T-duality of AdSd≤3 families by Poisson-Lie T-duality (arXiv:2111.07700)

    diff, v28, current

  25. Adding what might have been intended as the reference for a comment.

    Christian Ferko

    diff, v30, current

    • CommentRowNumber26.
    • CommentAuthorUrs
    • CommentTimeJun 8th 2024
    • (edited Jun 8th 2024)

    Thanks for this.

    I have added further bibdata and moved the item up to the list of original articles.

    diff, v31, current

1 to 26 of 26

  1.