Complete Spectrum of Long Operators in N=4 SYM at One Loop

TL;DR

This paper constructs the complete one-loop spectral curve for local operators in N=4 SYM, including fermions and derivatives, and relates it to classical string theory limits, introducing new bound states and demonstrating Bethe equation equivalences.

Contribution

It provides the full spectral curve for arbitrary operators in N=4 SYM at one loop, including fermions and derivatives, and introduces stacks and Bethe equation equivalences.

Findings

Spectral curve matches the Frolov-Tseytlin limit of classical strings.

Introduction of stacks as bound states of roots.

Proved equivalence of different Bethe equation formulations.

Abstract

We construct the complete spectral curve for an arbitrary local operator, including fermions and covariant derivatives, of one-loop N=4 gauge theory in the thermodynamic limit. This curve perfectly reproduces the Frolov-Tseytlin limit of the full spectral curve of classical strings on AdS_5xS^5 derived in hep-th/0502226. To complete the comparison we introduce stacks, novel bound states of roots of different flavors which arise in the thermodynamic limit of the corresponding Bethe ansatz equations. We furthermore show the equivalence of various types of Bethe equations for the underlying su(2,2|4) superalgebra, in particular of the type "Beauty" and "Beast".