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

Domenico Fiorenza, Hisham Sati, Urs Schreiber

Research output: Contribution to journalArticle

Abstract

We compute the L-theoretic dimensional reduction of the F1/Dp-brane super L-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-algebras are naturally related by an L-isomorphism which we find to act on the super p-brane cocycles by the infinitesimal version of the rules of topological T-duality and inducing an isomorphism between K0 and K1, rationally. In particular this is a derivation of the Buscher rules for RR-fields (Hori's formula) from first principles. Moreover, we show that these L-algebras are the homotopy quotients of the RR-charge coefficients by the "T-duality Lie 2-algebra". We find that the induced L-extension is a gerby extension of a 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)-dimensional super Lie algebra. Finally we observe that this satisfies expected properties of a local model space for F-theory elliptic fibrations.

Original languageEnglish (US)
Pages (from-to)1209-1270
Number of pages62
JournalAdvances in Theoretical and Mathematical Physics
Volume22
Issue number5
StatePublished - Jan 1 2018

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Cocycle
Branes
Duality
algebra
Lie Superalgebra
Algebra
Isomorphism
Coefficient
isomorphism
Elliptic Fibration
Dimensional Reduction
K-theory
First-principles
coefficients
Homotopy
Quotient
Fold
Correspondence
Space-time
Charge

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

Cite this

T-Duality from super Lie n-algebra cocycles for super p-branes. / Fiorenza, Domenico; Sati, Hisham; Schreiber, Urs.

In: Advances in Theoretical and Mathematical Physics, Vol. 22, No. 5, 01.01.2018, p. 1209-1270.

Research output: Contribution to journalArticle

Fiorenza, Domenico ; Sati, Hisham ; Schreiber, Urs. / T-Duality from super Lie n-algebra cocycles for super p-branes. In: Advances in Theoretical and Mathematical Physics. 2018 ; Vol. 22, No. 5. pp. 1209-1270.
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