Spinning superstrings at two loops: strong-coupling corrections to dimensions of large-twist SYM operators

TL;DR

This paper computes two-loop strong-coupling corrections to the energy of large-spin string states in AdS/CFT, providing insights into the matching between string theory and gauge theory in a specific scaling limit.

Contribution

It introduces a framework for calculating higher loop corrections to multi-spin string energies and matches two-loop string results with gauge theory predictions in a particular limit.

Findings

Two-loop correction agrees with Alday and Maldacena's proposal.

Resummation of logarithmic terms may be needed for interpolation.

Finite renormalization affects the relation between parameters and charges.

Abstract

We consider folded spinning strings in AdS_5xS^5 (with one spin component S in AdS_5 and J in S^5) corresponding to the Tr(D^S Z^J) operators in the sl(2) sector of the N=4 SYM theory in the special scaling limit in which both the string mass M ~ \sqrt \lambda \ln S and J are sent to infinity with their ratio fixed. Expanding in the parameter \el= J/M we compute the 2-loop string sigma model correction to the string energy and show that it agrees with the expression proposed by Alday and Maldacena in arxiv:0708.0672. We suggest that a resummation of the logarithmic \el^2 \ln^n \el terms is necessary in order to establish an interpolation to the weakly coupled gauge theory results. In the process, we set up a general framework for the calculation of higher loop corrections to the energy of multi-spin string configurations. In particular, we find that in addition to the direct 2-loop term in the string energy there is a contribution from lower loop order due to a finite ``renormalization'' of the relation between the parameters of the classical solution and the fixed spins, i.e. the charges of the SO(2,4) x SO(6) symmetry.