Rational three-spin string duals and non-anomalous finite size effects

TL;DR

The paper computes the non-anomalous finite-size (1/J) corrections to the one-loop conformal dimensions of operators dual to rational three-spin strings on S^5 by a one-line Bethe-ansatz method, relating them to spin-chain resolvents. It shows that these finite-size corrections reproduce the leading zero-mode piece of the corresponding string-theory one-loop energy for stable two-equal-spin cases, thereby strengthening the gauge/string correspondence at this order. The authors also develop a framework to generate higher conserved charges via resolvents and analyze branch-cut structures, identifying invariant structures and special parameter points. The results extend previous two-spin cases and provide insights for further matching with string theory, including potential anomalous corrections to be tackled in Beisert et al. 2005.

Abstract

We determine by a one line computation the one-loop conformal dimension and the associated non-anomalous finite size correction for all operators dual to spinning strings of rational type having three angular momenta (J_1,J_2,J_3) on S^5. Finite size corrections are conjectured to encode information about string sigma model loop corrections to the spectrum of type IIB superstrings on AdS_5xS^5. We compare our result to the zero-mode contribution to the leading quantum string correction derived for the stable three-spin string with two out of the three spin labels identical and observe agreement. As a side result we clarify the relation between the Bethe root description of three-spin strings of the type (J,J',J') with respectively J>J' and J<J'.