Exact computation of one-loop correction to energy of pulsating strings in AdS_5 x S^5

TL;DR

This work extends exact one-loop energy computations to pulsating strings in AdS$_5 imes$S$^5$, showing that their fluctuation problems reduce to single-gap Lamé operators and enabling closed-form determinants via stability angles. Building on prior results for folded strings, the authors develop a unifying semiclassical framework for time-periodic, integrable string solutions and relate it to the DHN quantization prescription. They derive explicit short-string expansions, revealing universal structures in the leading transcendental terms (e.g., logs and zeta-values) across pulsating and folded elliptic solutions, with clear implications for the strong-coupling behavior of dual gauge theory dimensions. The paper provides detailed analyses for pulsating strings in ${ m I extbf{R}} imes S^{2}$ and $AdS_3$, and for the folded string in ${ m R} imes S^{2}$, together with appendices that elucidate fluctuation Lagrangians, perturbative stability angles, and boundary-condition subtleties, thereby strengthening the bridge between semiclassical string theory and integrability-based approaches to AdS/CFT.

Abstract

In the present paper, which is a sequel to arXiv:1001:4018, we compute the one-loop correction to the energy of pulsating string solutions in AdS_5 x S^5. We show that, as for rigid spinning string elliptic solutions, the fluctuation operators for pulsating solutions can be also put into the single-gap Lame' form. A novel aspect of pulsating solutions is that the one-loop correction to their energy is expressed in terms of the stability angles of the quadratic fluctuation operators. We explicitly study the "short string" limit of the corresponding one-loop energies, demonstrating a certain universality of the form of the energy of "small" semiclassical strings. Our results may help to shed light on the structure of strong-coupling expansion of anomalous dimensions of dual gauge theory operators.