Luescher formula for GKP string

TL;DR

This paper develops a new framework for calculating finite-size corrections to large-spin operators in N=4 SYM, using a GKP string perspective and Luescher corrections, providing insights across coupling regimes.

Contribution

It introduces a Luescher correction-based formula for large-spin anomalous dimensions, complementing the spin-chain approach and applicable at any coupling.

Findings

The formalism predicts corrections starting at lower loop levels than traditional methods.

It matches known results up to five loops at weak coupling.

The approach aligns with string theory expectations at strong coupling.

Abstract

We investigate finite-size corrections to anomalous dimensions of large-spin twist-two operators in the planar maximally supersymmetric Yang-Mills theory. We develop a framework for analysis of these corrections, that is complementary to the conventional spin-chain approach, by making use of the hole rather than the magnon picture. From the dual string theory perspective where the large-spin operator is identified with the Gubser-Klebanov-Polyakov (GKP) string, our approach is equivalent to constructing the first Luescher correction to the energy of the GKP string by incorporating the contribution of virtual excitations propagating on it. It allows us to propose a formula that controls a particular class of large-spin corrections to the twist-two anomalous dimension and holds at any value of the coupling constant. Compared to wrapping corrections computed with magnons propagating on the spin chain, the finite-size corrections that are encoded in our formalism start at a lower loop level. Our formalism thus calls for modification of the asymptotic contributions which are conventionally incorporated within the Asymptotic Bethe Ansatz. An educated guess allows us to remedy this pitfall and successfully confront our predictions with known results up to five loop accuracy at weak coupling. Finally, our formula sheds light on the weak-to-strong coupling transition for the subleading large-spin corrections under study and confirms stringy expectations at strong coupling where they are found to be identical to the first Luescher correction to the vacuum energy of the O(6) sigma model.