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We construct the exceptional sigma model: a two-dimensional sigma model coupled to a supergravity background in a manifestly (formally) ED(D)-covariant manner. This formulation of the background is provided by exceptional field theory (EFT), which unites the metric and form fields of supergravity in ED(D) multiplets before compactification. The realization of the symmetries of EFT on the world sheet uniquely fixes the Weyl-invariant Lagrangian and allows us to relate our action to the usual type-IIA fundamental string action and a form of the type-IIB (m, n) action. This uniqueness "predicts" the correct form of the couplings to gauge fields in both Neveu-Schwarz and Ramond sectors, without invoking supersymmetry.
Bibliographical note5 pages. V2: minor corrections, refs added