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Flat currents of the Green-Schwarz superstrings in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi><mml:mi>d</mml:mi><mml:msub><mml:mi>S</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:msup><mml:mi>S</mml:mi><mml:mn>1</mml:mn></mml:msup></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>A</mml:mi><mml:mi>d</mml:mi><mml:msub><mml:mi>S</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:…
We construct a one-parameter family of flat currents in $Ad{S}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{1}$ and $Ad{S}_{3}\ifmmode\times\else\texttimes\fi{}{S}^{3}$ Green-Schwarz superstrings, which would naturally lead to a hierarchy of classical conserved nonlocal charges. In the former case we rewrite the $Ad{S}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{1}$ string using a new ${\mathbb{Z}}_{4}$-graded base of the superalgebra $su(2,2|2)$. In both cases the existence of …