Green-Schwarz action for Type IIA strings on $AdS_4\times CP^3$

TL;DR

This work constructs a Green-Schwarz action for Type IIA strings on $AdS_4\\times CP^3$ by exploiting a ${\\sf Z}_4$ automorphism of the coset $OSp(4|6)/(SO(1,3)\\times SU(3)\\times U(1))$, yielding a ${\\sf Z}_4$-graded current formulation. The action reduces to the $AdS_4\\times CP^3$ bosonic sigma-model upon truncation, preserves $24$ supersymmetries, and exhibits local $\\kappa$-symmetry, which gauges away eight real fermions to leave $16$ physical fermions. A Lax connection with spectral-parameter dependence is constructed, proving classical integrability and enabling an infinite hierarchy of conserved charges via the monodromy matrix. The authors also discuss extensions to related backgrounds and the implications for the $AdS_4$/CFT$_3$ program and ABJM-like dualities, suggesting a robust algebraic framework for integrable string theories in these geometries.

Abstract

We present the Green-Schwarz action for Type IIA strings on $AdS_4\times CP^3$. The action is based on a $\Zop_4$ automorphism of the coset $OSp(4|6)/(SO(1,3)\times SU(3)\times U(1))$. The equations of motion admit a representation in terms of a Lax connection, showing that the system is classically integrable.