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arXiv · 0811.1566

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

Jaume Gomis·Dmitri Sorokin·Linus Wulff
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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.

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Jaume Gomis, Dmitri Sorokin, Linus Wulff. 2009-02-03. The complete AdS(4) x CP(3) superspace for the type IIA superstring and D-branes. https://doi.org/10.1088/1126-6708%2F2009%2F03%2F015

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