Bethe ansatz and fluctuations in SU(3) Yang-Mills operators

TL;DR

This paper uses the Bethe ansatz to compute quantum corrections to the anomalous dimensions of scalar operators in SU(3) Yang-Mills theory, linking gauge theory results with string theory predictions in AdS_5xS^5.

Contribution

It applies the Bethe ansatz to calculate quantum corrections for scalar operators with three angular momenta, extending previous work to the SU(3) sector.

Findings

Computed anomalous dimensions matching string energy corrections

Identified quantum corrections for operators with two equal angular momenta

Established a link between gauge theory and string theory predictions

Abstract

We consider the scalar operators corresponding to semiclassical string states in AdS_5xS^5 with the three angular momenta in S^5 non-trivial. The string states recieve quantum corrections and we study the corresponding process on the gauge theory side. The anomalous dimension of the scalar operators is computed using the Bethe ansatz and we find the correction that corresponds to the energy of the quantized string. We restrict for simplicity to the case where two of the angular momenta in S^5 are equal.