TY - JOUR

T1 - T-Duality from super Lie n-algebra cocycles for super p-branes

AU - Fiorenza, Domenico

AU - Sati, Hisham

AU - Schreiber, Urs

N1 - Publisher Copyright:
© 2018 International Press of Boston, Inc.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

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U2 - 10.4310/atmp.2018.v22.n5.a3

DO - 10.4310/atmp.2018.v22.n5.a3

M3 - Article

AN - SCOPUS:85066037937

VL - 22

SP - 1209

EP - 1270

JO - Advances in Theoretical and Mathematical Physics

JF - Advances in Theoretical and Mathematical Physics

SN - 1095-0761

IS - 5

ER -