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

TL;DR

This paper computes one-loop conformal dimensions and finite size corrections for three-spin string operators in AdS_5xS^5, providing insights into string spectrum corrections and clarifying Bethe root descriptions.

Contribution

It presents a simple computation of finite size corrections for all three-spin rational string operators, linking them to string sigma model loop corrections and clarifying Bethe root relations.

Findings

Finite size corrections encode string loop effects.

Agreement with quantum string correction for specific three-spin strings.

Clarification of Bethe root descriptions for three-spin strings.

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'.