Flat Currents of the Green-Schwarz Superstrings in AdS_5 x S^1 and AdS_3 x S^3 backgrounds

Abstract

We construct a one-parameter family of flat currents in AdS_5 x S^1 and AdS_3 x S^3 Green-Schwarz superstrings, which would naturally lead to a hierarchy of classical conserved nonlocal charges. In the former case we rewrite the AdS_5 x S^1 string using a new Z_4-graded base of the superalgebra su(2,2|2). In both cases the existence of the Z_4 grading in the superalgebras plays a key role in the construction. As a result, we find that the flat currents, when formally written in terms of the G_0-gauge invariant lowercase 1-forms, take the same form as the one in AdS_5 x S^5 case.

18 pages, LaTeX file. References added and typos corrected

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• A note about fermionic equations of AdS_4 x CP^3 superstring
• Solution Transformations for GS String in AdS_5 x S^5 by Conserved Quantities