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PreprintarXiv licencearXiv

Birth and Death in Two-color ABJM

  • Marco S. Bianchi
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Abstract

We solve exactly the leading quantum deformation of the two-point metric of half-BPS operators in U(2)× 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.

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Cite

BibTeXRIS
BibTeX
@misc{bianchi2026birth,
  title = {{Birth and Death in Two-color ABJM}},
  author = {Marco S. Bianchi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05653},
  eprint = {2609.05653},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05653},
}
RIS
TY  - UNPB
TI  - Birth and Death in Two-color ABJM
AU  - Marco S. Bianchi
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.05653
UR  - https://arxiv.org/abs/2609.05653
AB  - We solve exactly the leading quantum deformation of the two-point metric of half-BPS operators in U(2)× 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.
ER  -