Matching Higher Conserved Charges for Strings and Spins

TL;DR

This paper demonstrates that the agreement between gauge theory operators and string energies extends to an infinite set of higher conserved charges, highlighting deep integrable structure correspondence in AdS/CFT.

Contribution

It shows the matching of higher conserved charges between gauge theory and string theory, using integrable techniques on both sides, advancing the understanding of AdS/CFT integrability.

Findings

Agreement of higher conserved charges between gauge and string theories

Construction of generating functions for charges using integrable methods

Extension of one-loop scaling dimension matching to all higher charges

Abstract

We demonstrate that the recently found agreement between one-loop scaling dimensions of large dimension operators in N=4 gauge theory and energies of spinning strings on AdS_5 x S^5 extends to the eigenvalues of an infinite number of hidden higher commuting charges. This dynamical agreement is of a mathematically highly intricate and non-trivial nature. In particular, on the gauge side the generating function for the commuting charges is obtained by integrable quantum spin chain techniques from the thermodynamic density distribution function of Bethe roots. On the string side the generating function, containing information to arbitrary loop order, is constructed by solving exactly the Backlund equations of the integrable classical string sigma model. Our finding should be an important step towards matching the integrable structures on the string and gauge side of the AdS/CFT correspondence.