Full Lagrangian and Hamiltonian for quantum strings on AdS_4 x CP^3 in a near plane wave limit

TL;DR

This paper derives the complete interacting Lagrangian and Hamiltonian for quantum strings in a near plane wave limit of AdS_4 x CP^3, including curvature corrections up to quartic order, using a superspace approach and careful gauge fixing.

Contribution

It provides the first full explicit form of the interacting Hamiltonian for quantum strings in this background, incorporating curvature effects and fermionic constraints.

Findings

Derived the full interacting Lagrangian with cubic and quartic terms.

Constructed the Hamiltonian using Dirac and Poisson brackets with fermionic constraints.

Presented a consistent gauge fixing and field redefinitions for simplifying the Hamiltonian.

Abstract

We find the full interacting Lagrangian and Hamiltonian for quantum strings in a near plane wave limit of AdS_4 x CP^3. The leading curvature corrections give rise to cubic and quartic terms in the Lagrangian and Hamiltonian that we compute in full. The Lagrangian is found as the type IIA Green-Schwarz superstring in the light-cone gauge employing a superspace construction with 32 grassmann-odd coordinates. The light-cone gauge for the fermions is non-trivial since it should commute with the supersymmetry condition. We provide a prescription to properly fix the kappa-symmetry gauge condition to make it consistent with light-cone gauge. We use fermionic field redefinitions to find a simpler Lagrangian. To construct the Hamiltonian a Dirac procedure is needed in order to properly keep into account the fermionic second class constraints. We combine the field redefinition with a shift of the fermionic phase space variables that reduces Dirac brackets to Poisson brackets. This results in a completely well-defined and explicit expression for the full interacting Hamiltonian up to and including terms quartic in the number of fields.