Hamiltonian of Green—Schwarz IIB Superstring Theory in AdS3 × S3 Background

Abstract

We parameterize the Green-Schwarz IIB superstring in the AdS3 × S3 background under the light cone gauge by the method of Metsaev and Tseytlin in AdS3 and by the method of Rahmfeld and Rajaraman in S3. After some calculation, we obtain the corresponding Maurer—Cartan 1-forms and the action. Then we fix two bosonic variables x+ = τ and y5 = σ, perform the partial Legendre transformation of the remaining bosonic variables, and find a Lagrangian that is linear in velocity after eliminating the metric of the world sheet. We also give the Hamiltonian and prove that the system is local and the Poisson bracket of the theory can be well defined. Using these results, one can further study the properties of solution space, solution transformation and the structure of the flat current algebra of the superstring in the AdS3 × S3 background.