Flat Currents of Green—Schwarz Superstring in AdS ₃ × S ³ under Symmetry Transformations

Abstract

We show that for Green-Schwarz superstring in 𝐴𝑑𝑆3 × 𝑆 3 , the one-parameter family of flat currents retains a zero-curvature condition and keeps the variation relations under 𝜅-symmetry, diffeomorphism, local Lorentz 𝑆𝑂(1, 2) × 𝑆𝑂(3) and global 𝑃 𝑆𝑈 (1, 1|2) 2 symmetry transformations respectively. This indicates that the flat currents exist in all the 𝜅-symmetry gauge fixed cases. As a result, we find that the infinite conserved quantities are invariant under these transformations and independent of the gauge choice of the system.

Hamiltonian of Green—Schwarz IIB Superstring Theory in AdS 3 × S 3 Background

“…Its flat current was discussed in Refs. [24,25]. An alternative "hybrid" approach to quantization of a superstring in AdS 3 × S 3 was developed in Refs.…”