The worldsheet low-energy limit of the AdS_4 x CP^3 superstring

TL;DR

The paper derives the worldsheet infrared effective theory of the AdS$_4\times$CP$^3$ superstring in the spinning-string limit, where massless worldsheet modes dominate. It shows coset constructions are insufficient in this limit and constructs the full Green–Schwarz action, proceeding to a careful low-energy expansion around the spinning-string background. The main result is a CP$^3$ nonlinear sigma model coupled to a Dirac fermion, with bosons constrained to $S^7$ ($\sum_j|z^j|^2=1$) and a non-dynamical U(1) gauge field that yields the Fubini–Study form; the action reads $\mathcal{L} = \eta^{\alpha\beta}\overline{D_\alpha z^j}\,D_\beta z^j + i\overline{\Psi}\gamma^\alpha\widehat{D}_\alpha\Psi + \tfrac14(\overline{\Psi}\gamma^\alpha\Psi)^2$. The derivation relies on a reduction from M-theory on AdS$_4\times S^7$, Hopf fibration to CP$^3$, and a decompactified worldsheet, providing a concrete IR effective theory for the ABJM-related string dynamics with potential links to integrability and Bethe Ansatz results.

Abstract

We consider the AdS_4 x CP^3 IIA superstring sigma-model in the background of the "spinning string" classical solution, which possesses two Noether spins. In the limit when one of the spins is infinite there are massless excitations, which govern the infrared worldsheet properties of the model. We obtain a sigma-model of CP^3 with fermions, which describes the dynamics of these massless modes.