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Comparing<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>duality to string/<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mo>(</mml:mo><mml:mi>D</mml:mi><mml:mi>โ</mml:mi><mml:mn>5</mml:mn><mml:mo>)</mml:mo></mml:math>-brane duality on actions
We realize the string/$(D\ensuremath{-}5)$-brane duality on the action at the classical level between the ${T}^{10\ensuremath{-}D}$-compactified heterotic string effective action and the $(D\ensuremath{-}5)$-brane effective action in $D$ dimensions by managing a Lagrange multiplier field. In the same way the $S$ duality is also reconstructed as a dual transformation on the ${T}^{6}$-compactified โฆ