Sugawara form for AdS superstring

We show that the stress-energy tensor for a superstring in the AdS5×S5 background is written in a supersymmetric generalized “Sugawara” form. It is the “supertrace” of the square of the right-invariant current which is the Noether current satisfying the flatness condition. The Wess-Zumino term is taken into account through the supersymmetric gauge connection in the right-invariant currents, therefore the obtained stress-energy tensor is κ invariant. The integrability of the AdS superstring provides an infinite number of the conserved “local” currents which are supertraces of the nth power of the right-invariant current. For even n the “local” current reduces to terms proportional to the Virasoro constraint and the κ symmetry constraint, while for odd n it reduces to a term proportional to the κ symmetry constraint.