Spiky Strings on AdS(4) X CP**3

TL;DR

This work extends the study of integrable string dynamics to the AdS$_4\times{\bf CP}^3$ background by examining rigidly rotating strings in the diagonal SU(2) subsector, effectively reducing to a rotating string on $R\times S'^2$. By solving the Polyakov action and Virasoro constraints, the authors derive the general conserved charges and identify two key infinite-size limits: the giant magnon and the spike, with corresponding dispersion relations. The giant magnon satisfies $E - J = \sqrt{2\lambda}\,|\sin(p/2)|$, while the spike is characterized by a finite $J$ with $E - \Delta\phi$ dispersion and exponential finite-size corrections. Finite-size effects are computed explicitly via elliptic integrals, providing a detailed semiclassical account of these excitations and paving the way for further exploration of multi-spin generalizations and scattering in the ABJM context.

Abstract

We study a giant magnon and a spike solution for the string rotating on AdS(4) X CP**3 geometry. We consider rigid rotating fundamental string in the SU(2) X SU(2) sector inside the CP**3 and find out the general form of all the conserved charges. We find out the dispersion relation corresponding to both the known giant magnon and the new spike solutions. We further study the finite size correction in both cases.