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• 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.

• 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, $String(G)$?

• 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 $SU(2)$. 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

• 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)
• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeOct 24th 2018

• 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.

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

Anonymous

• 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.

• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeJan 15th 2019

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

• 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 $\alpha'$ and the string coupling constant $g_s$, 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 $g_s$; and already a genus-0 (tree level) it apparently breaks down for the open string (i.e. on punctured disks) at some order of $\alpha'$.

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