
I will revisit the spectrum of singletrace operators in N=4 SYM, and describe how to classify the irreducible representations of the superconformal symmetry that they form, in terms of a noncompact generalisation of Young diagrams. These multiplets are in onetoone correspondence to “rational” solutions to a Qsystem. Traditionally, this Qsystem is defined by the algebra in question, but I will argue that it lives a more natural, algebraindependent life on the corresponding Young diagram. Using this intuition, I will present a simple algorithm to solve such systems, providing a cleaner and more powerful alternative to Bethe equations. These solutions form the starting point for perturbative calculations of anomalous dimensions via the Quantum Spectral Curve. I will sketch a conceptually very simple method to do such calculations for general states, discuss patterns in the results, and speculate about how to get more info out of the QSC.
