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

TL;DR

This paper constructs a family of flat currents in specific superstring backgrounds, revealing conserved charges and highlighting the role of Z_4 grading in superalgebras, extending known structures from AdS_5 x S^5.

Contribution

It introduces a new flat current construction for superstrings in AdS_5 x S^1 and AdS_3 x S^3, utilizing a Z_4 grading approach to generalize integrability features.

Findings

Established flat currents in AdS_5 x S^1 and AdS_3 x S^3 backgrounds.

Demonstrated the role of Z_4 grading in superalgebra structures.

Showed the similarity of flat currents to the AdS_5 x S^5 case.

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.