Stringing Spins and Spinning Strings

TL;DR

This paper uses integrable spin chain techniques to compute one-loop anomalous dimensions of certain operators in N=4 Super Yang-Mills, revealing cases where gauge theory results match or differ from string theory predictions.

Contribution

It applies integrable methods to analyze anomalous dimensions of operators, identifying cases with and without BMN limits and comparing results to string theory predictions.

Findings

Computed anomalous dimensions for operators with large scalar fields.

Found discrepancies with previous semiclassical string results in some cases.

Confirmed consistency with string fluctuation spectra in certain operators.

Abstract

We apply recently developed integrable spin chain and dilatation operator techniques in order to compute the planar one-loop anomalous dimensions for certain operators containing a large number of scalar fields in N =4 Super Yang-Mills. The first set of operators, belonging to the SO(6) representations [J,L-2J,J], interpolate smoothly between the BMN case of two impurities (J=2) and the extreme case where the number of impurities equals half the total number of fields (J=L/2). The result for this particular [J,0,J] operator is smaller than the anomalous dimension derived by Frolov and Tseytlin [hep-th/0304255] for a semiclassical string configuration which is the dual of a gauge invariant operator in the same representation. We then identify a second set of operators which also belong to [J,L-2J,J] representations, but which do not have a BMN limit. In this case the anomalous dimension of the [J,0,J] operator does match the Frolov-Tseytlin prediction. We also show that the fluctuation spectra for this [J,0,J] operator is consistent with the string prediction.