Review of AdS/CFT Integrability, Chapter III.5: Luscher corrections

TL;DR

This paper reviews the generalization of Luscher corrections, which account for finite-size effects in integrable quantum field theories, and their application to the AdS/CFT correspondence, specifically in string theory and N=4 SYM.

Contribution

It provides a comprehensive review of how Luscher corrections are extended to complex dispersion relations and multiparticle states within the AdS/CFT framework.

Findings

Generalized Luscher corrections for complex dispersion relations.

Application to worldsheet QFT of superstring in AdS5xS5.

Insights into anomalous dimensions in N=4 SYM.

Abstract

In integrable quantum field theories the large volume spectrum is given by the Bethe Ansatz. The leading corrections, due to virtual particles circulating around the cylinder, are encoded in so-called Luscher corrections. In order to apply these techniques to the AdS/CFT correspondence one has to generalize these corrections to the case of generic dispersion relations and to multiparticle states. We review these various generalizations and the applications of Luscher's corrections to the study of the worldsheet QFT of the superstring in AdS5xS5 and, consequently, to anomalous dimensions of operators in N=4 SYM theory.