Spin-Bits and N=4 SYM

TL;DR

This paper reviews the spin-bit formalism for non-planar dynamics in N=4 Super Yang-Mills theory, focusing on the su(2) sector, and proposes an algorithmic approach to extend planar results to non-planar cases.

Contribution

It introduces an algorithmic deplanarizing procedure for local operators, enabling the formulation of higher-loop su(2) spin-bit Hamiltonians in N=4 SYM.

Findings

Developed a deplanarizing algorithm for local operators.

Formulated testable conjectures for higher-loop Hamiltonians.

Extended the spin-bit formalism to non-planar regimes.

Abstract

We briefly review the spin-bit formalism, describing the non-planar dynamics of the $\mathcal{N}=4,d=4$ Super Yang-Mills SU(N) gauge theory. After considering its foundations, we apply such a formalism to the $su(2)$ sector of purely scalar operators. In particular, we report an algorithmic formulation of a deplanarizing procedure for local operators in the planar gauge theory, used to obtain planarly-consistent, testable conjectures for the higher-loop $su(2)$ spin-bit Hamiltonians. Finally, we outlook some possible developments and applications.