Interacting Double Coset Magnons

TL;DR

This paper studies the anomalous dimensions of certain nearly BPS operators in N=4 SYM, revealing magnon interactions at two loops through detailed analysis of operator mixing involving giant gravitons and strings.

Contribution

It introduces the first correction to magnon interactions at two loops in a nearly BPS sector, extending understanding of operator mixing in AdS/CFT correspondence.

Findings

Magnon interactions appear at two loops in the dilute gas regime.

Operator mixing is explicitly analyzed for two giant gravitons with four strings.

Non-zero corrections modify the integrable magnon picture at higher loops.

Abstract

We consider the anomalous dimensions of restricted Schur polynomials constructed using n~O(N) complex adjoint scalars Z and m complex adjoint scalars Y. We fix m<<n so that our operators are almost half BPS. At leading order in m/n this system corresponds to a dilute gas of m free magnons. Adding the first correction of order m/n to the anomalous dimension, which arises at two loops, we find non-zero magnon interactions. The form of this new operator mixing is studied in detail for a system of two giant gravitons with four strings attached.