Iterative Structure of the N=4 SYM Spin Chain

Understand

We develop algebraic methods for finding loop corrections to the N=4 SYM dilatation generator, within the noncompact psu(1,1|2) sector.

• This sector gives a 't Hooft coupling lambda-dependent representation of psu(1,1|2) times psu(1|1)^2.
• At first working independently of the representation, we present an all-order algebraic ansatz for the lambda-dependence of this Lie algebra's generators.
• The ansatz solves the symmetry constraints if an auxiliary generator, h, satisfies certain simple commutation relations with the Lie algebra generators.