Spinning Pulsating String Solitons in AdS_5 x S^5

TL;DR

The paper constructs new classical string solitons in $AdS_5\times S^5$ where spin and pulsation are nontrivially coupled, introducing an amplitude-related constant that shifts energy–spin and energy–R-charge scaling. Using ansätze that render the worldsheet equations integrable, the solutions are expressed analytically in terms of elliptic functions, offering detailed energy and charge relations in various limits. It presents several configurations: spinning in $AdS_5$ with pulsation in $S^5$, the converse, and pulsating multi-spin generalizations, each yielding novel scaling laws distinct from previously known results. The work lays groundwork for potential dual Yang–Mills operator identifications and invites further study of stability and quantum corrections in these pulsating-spinning sectors.

Abstract

We point out the existence of some simple string solitons in AdS_5 x S^5, which at the same time are spinning in AdS_5 and pulsating in S^5, or vice-versa. This introduces an additional arbitrary constant into the scaling relations between energy and spin or R-charge. The arbitrary constant is not an angular momentum, but can be related to the amplitude of the pulsation. We discuss the solutions in detail and consider the scaling relations. Pulsating multi spin or multi R-charge solutions can also be constructed.