An article that we have written:
Domenico Fiorenza, Hisham Sati, Urs Schreiber,
T-duality in rational homotopy theory via $L_\infty$-algebras
GTMP 1 (2018) 42-76
download:
journal pdf
on rational topological T-duality in superstring theory formulated via L-∞ algebras.
Abstract We combine Sullivan models from rational homotopy theory with Stasheff‘s L-∞ algebras to describe a duality in string theory. Namely, what in string theory is known as topological T-duality between K0-cocycles in type IIA string theory and K1-cocycles in type IIB string theory, or as Hori’s formula, may be recognized as a Fourier-Mukai transform between twisted cohomologies when regarded through the lenses of rational homotopy theory. We show this as an example of topological T-duality in rational homotopy theory, which in turn can be completely formulated in terms of morphisms of L-∞ algebras.
Other contributions in this volume:
Ours is a review, making the Fourier-Mukai transform manifest, of
Talk slides:
Rational topological T-duality: pdf (talk by Domenico Fiorenza at LMS midlands meeting 2017)
Super p-Brane Theory emerging from Super Homotopy-Theory (talk at StringMath 2017)
Super topological T-Duality (talk at Regensburg)
Lecture notes:
This is based on our previous articles:
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