Complete spectrum of long operators in Script N = 4 SYM at one loop

Abstract

We construct the complete spectral curve for an arbitrary local operator, including fermions and covariant derivatives, of one-loop = 4 gauge theory in the thermodynamic limit. This curve perfectly reproduces the Frolov-Tseytlin limit of the full spectral curve of classical strings on AdS5 × S5 derived in [64]. 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 (2,2|4) superalgebra, in particular of the type ``Beauty'' and ``Beast''.