Handling Handles. Part II. Stratification and Data Analysis

Understand

In a previous work, we proposed an integrability setup for computing non-planar corrections to correlation functions in $\mathcal{N}=4$ super Yang-Mills theory at any value of the coupling constant.

• The procedure consists of drawing all possible tree-level graphs on a Riemann surface of given genus, completing each graph to a triangulation, inserting a hexagon form factor into each face, and summing over a complete set of states on each edge of the triangulation.
• The summation over graphs can be interpreted as a quantization of the string moduli space integration.
• The quantization requires a careful treatment of the moduli space boundaries, which is realized by subtracting degenerate Riemann surfaces; this procedure is called stratification.