Schreiber T-Duality from super Lie n-algebra cocycles for super p-branes

An article that we have written:

Abstract. We compute the L-infinity-theoretic double dimensional reduction of the F1/Dpp-brane super L L_\infty-cocycles with coefficients in rationalized twisted K-theory from the 10d type IIA and type IIB super Lie algebras down to 9d. We show that the two resulting coefficient L L_\infty-algebras are naturally related by an L L_\infty-isomorphism which we find to act on the super pp-brane cocycles by the infinitesimal version of the rules of topological T-duality and inducing an isomorphism between K 0K^0 and K 1K^1, rationally. Moreover, we show that these L L_\infty-algebras are the homotopy quotients of the RR-charge coefficients by the “T-duality Lie 2-algebra”. We find that the induced L L_\infty-extension is a gerby extension of a 9+(1,1)9+(1,1) dimensional (i.e. “doubled”) T-duality correspondence super-spacetime, which serves as a local model for T-folds. We observe that this still extends, via the D0-brane cocycle of its type IIA factor, to a 10+(1,1)10+(1,1)-dimensional super Lie algebra. Finally we show that this satisfies all the expected properties of a local model space for F-theory elliptic fibrations.


Talk slides:


of the underlying rational topological T-duality:

Lecture notes:

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