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We review and elaborate on the issue of the dilaton transformation under the usual r → α′/r target space duality and its "non-static" generalization (or σ-model duality). It is found that the transformation law r → α′/r, [Formula: see text] which guarantees duality at the one-loop σ-model level should be modified at two (and higher) loop order. The "non-static" duality is illustrated on the example of "cosmological" solutions in D ≥ 2 with time-dependent radii of space torus.
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A.A. Tseytlin (1991) studied this question.
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