Birth and Death in Two-color ABJM

Abstract

We solve exactly the leading quantum deformation of the two-point metric of half-BPS operators in $U(2)\times U(2)$ ABJM theory at finite rank. In the natural coupling-independent Schur frame, its tree-normalized two-loop correction is a Jacobi operator on the chain of two-row Young diagrams. A ground-state transform maps it to a reversible birth--death process whose stationary distribution is the Plancherel measure conditioned on diagrams with at most two rows. Its eigenmodes are Racah polynomials, its large-$n$ limit approaches radial Ornstein--Uhlenbeck dynamics, and an equivalent two-spin description identifies the Jacobi operator with a restricted $SU(2)$ Casimir.