The complete AdS(4) x CP(3) superspace for the type IIA superstring and D-branes

TL;DR

This paper constructs the full superspace for type IIA superstring and D-branes in AdS_4 x CP^3, enabling detailed analysis of their dynamics and integrability beyond the supercoset approximation.

Contribution

It provides an explicit 10D superspace formulation of AdS_4 x CP^3, extending previous supercoset models to include all fermionic directions for superstring and D-brane actions.

Findings

Constructed the complete AdS_4 x CP^3 superspace with 32 Grassmann-odd directions.

Showed that the supercoset string action only describes a subsector of the full superstring.

Highlighted the need for more general methods to analyze classical integrability of the full superstring.

Abstract

We lift the bosonic AdS_4 x CP^3 solution of type IIA supergravity preserving 24 supersymmetries to a D=10 superspace which has 32 Grassmann-odd directions. The type IIA superspace is obtained from D=11 via dimensional reduction of the coset superspace OSp(8|4)/SO(7) x SO(1,3) by realizing the latter as a Hopf fibration over the former. This construction generalizes to superspace the Hopf fibration of S^7 as a U(1) bundle over CP^3, and is suitable for writing the explicit form of Green-Schwarz-type actions encoding the dynamics of the type IIA string and branes in the AdS_4 x CP^3 superbackground. We show that the OSp(6|4)/U(3) x SO(1,3) supercoset string action describes only a subsector of the complete Green-Schwarz superstring. Thus, even though the superstring equations of motion in the OSp(6|4)/U(3) x SO(1,3) subsector are classically integrable, the fact that the full AdS_4 x CP^3 superspace is not a supercoset requires the use of more general methods to determine whether the superstring in the complete AdS_4 x CP^3 superbackground is classically integrable.