T-duality in rational homotopy theory via $L_{\infty }$-algebras

Abstract

We combine Sullivan models from rational homotopy theory with Stasheff's $L_{\infty }$-algebras to describe a duality in string theory. Namely, what in string theory is known as topological T-duality between $K^0$-cocycles in type IIA string theory and $K^1$-cocycles in type IIB string theory, or as Hori's formula, can be recognized as a Fourier-Mukai transform between twisted cohomologies when looked 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 $L_{\infty }$-algebras.

A few inaccuracies fixed and one example added; 24 pages

References in corpus (2)

• Rational sphere valued supercocycles in M-theory and type IIA string theory
• $L_{i}nfty$ rational homotopy of mapping spaces

Cited by in corpus (4)

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