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Created:
A notion of connection for principal 2-bundles that does not impose the fake flatness condition.
See also the references at adjusted Weil algebra.
Definition of adjusted connections in terms of cocycle data:
Examples for T-duality:
Further references for T-duality:
Konrad Waldorf, Geometric T-duality: Buscher rules in general topology, arXiv:2207.11799.
Thomas Nikolaus, Konrad Waldorf, Higher geometry for non-geometric T-duals, arXiv:1804.00677.
Thanks a lot for providing the original sources. Is the “modified Weil algebra” the same as “adjusted Weil algebra”?
Is there a source that discusses adjusted connections in full generality of Lie ∞-groups?
Rist–Saemann–Wolf only discuss Lie 2-algebras, whereas your papers seem to talk only about String-like extensions, if I understood them correctly.
We actually called it the Chern-Simons -algebra (p. 48), because it brings out the expected Chern-Simons-terms in the – which is what the whole “adjustment”-process is about.
There is no sense of doing this for non-string-like extensions: These higher central extensions are what is classified by invariant polynomials transgressing to Chern-SImons elements. In accounts you may be looking at this may be hidden in the assumption of a bilinear invariant pairing: This is the binary invariant polynomial which classifies the String-like extension. Without such, there is no sense to adjust to any Chern-Simons terms.
The delooping of the smooth -group Lie integrating an -algebra is a truncation of the stackification of
This is the stacky formulation of Henriques’s notion of integration of -algebras. For Lie 1-algebras and using 1-truncation this reduces to the “path method” for Lie integration, which is for instance implicit in Brylinski & McLaughlin 1996.
The process we described enhances this Lie integration (in a way I have recalled when we discussed this last time) to a stack such that maps are (cocycles for) -principal -bundles on with non-fake flat -connection given by the expected Chern-Simons terms.
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