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We show that ${\cal N} = 4$ supersymmetric-Yang-Mills (SYM) theory on$\mathbb{R} \times S^3$ with gauge group $\text{SU}(N)$ is described in anear-BPS limit by a simple lower-dimensional nonrelativistic field theory with$\text{SU}(1,1) \times \text{U}(1)$ invariant interactions. In this limit, asingle complex adjoint scalar field survives, and part of its interaction isobtained by exactly integrating out the gauge boson of the SYM theory. Takinginto account normal ordering, the interactions match the one-loop dilatationoperator of the $\text{SU}(1,1)$ sector, establishing the consistency of thelimit at the quantum level. We discover a tantalizing field-theoreticstructure, corresponding to a $(1+1)$-dimensional complex chiral boson on acircle coupled to a nondynamical gauge field, both in the adjointrepresentation of $\text{SU}(N)$. The successful construction of alower-dimensional nonrelativistic field theory in the $\text{SU}(1,1)$ near-BPSlimit provides a proof of concept for other BPS bounds. These are expected tolead to richer field theories in nonrelativistic corners of ${\cal N} = 4$ SYMthat include fermions, gauge fields and supersymmetry and can provide a novelpath towards understanding strongly coupled finite-$N$ dynamics of gaugetheories.

Nonrelativistic Corners of ${\cal N} = 4$ Supersymmetric Yang--Mills Theory