Eliminating ambiguities for quantum corrections to strings moving in $AdS_4\times \mathbb{CP}^3$

TL;DR

The paper extends Nastase's physical principle for removing regularization ambiguities from two-dimensional solitons to long spinning strings in AdS$_4\times \mathbb{CP}^3$, aiming to obtain unambiguous, AdS/CFT-consistent one-loop corrections. By carefully identifying a mass-like parameter and employing derivative regularization within a large-$\omega$ expansion, the authors show that the regularization ambiguities that plagued earlier calculations can be eliminated, yielding results in agreement with AdS/CFT, and they explicitly connect the fluctuation spectrum to the soliton analysis. The work reproduces the McLoughlin et al. outcome in the appropriate limit and derives a holographically relevant function $h(\lambda)$, supporting the deeper link between string solitons and their dual gauge-theory descriptions. While technical hurdles limit complete computation to leading orders in certain parameters, the method provides a solid foundation for applying the same principle to other classical string solitons beyond the specific spinning string considered here.

Abstract

We apply a physical principle, previously used to eliminate ambiguities in quantum corrections to the 2 dimensional kink, to the case of spinning strings moving in $AdS_4\times \mathbb{CP}^3$, thought of as another kind of two dimensional soliton. We find that this eliminates the ambiguities and selects the result compatible with AdS/CFT, providing a solid foundation for one of the previous calculations, which found agreement. The method can be applied to other classical string "solitons".