Beyond the Fock Vacuum in Finite-N Bilocal Algebras of Vector Models
Abstract
We discuss the finite-N Hilbert space of bilocal operators that underlies bilocal holography of vector models, beyond the sector built on the Fock vacuum. If the microscopic oscillator Fock space carries a multiplicity-free dual action of a compact color group G and a bilocal algebra, Howe duality implies that projection to the derived subgroup [G,G] selects precisely the characters of the abelianization Gab=G/[G,G] that occur in the Fock space. Thus O(N)/SO(N)=ℤ2 gives two sectors, U(N)/SU(N)=U(1) gives integer determinant-charge sectors, while Sp(N) is perfect and gives no additional sector; Bose/Fermi statistics and the number of modes determine which sectors are actually realized. We construct the epsilon and determinant backgrounds that generate these sectors, together with their finite-N constraints and Casimirs, and find that the two bosonic O(N) sectors are not distinguished by any Casimir. Using group-integral projectors, we derive explicit sector-resolved characters for the O(N) and U(N) theories. Around each new background we solve the constraints with auxiliary oscillators, which form a Fermi sea for bosonic matter. In the free vector model on ℝ× S2 the new sectors consist of baryonic primaries; we determine their energies, degeneracies and spin content exactly at finite N, together with their lowest energy at fixed angular momentum.
Related
- Anticommuting Displacement Operators, Exact Pauli Algebras,and the Singlet State from the Oscillator Vacuum
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- Bilocal flows and universality with field-dependent regulators
- Finite-Time Bounds on Conformal Vacuum Energy Relaxation in Scalar-Tensor Gravity
BibTeX
@misc{ahn2026beyond,
title = {{Beyond the Fock Vacuum in Finite-$N$ Bilocal Algebras of Vector Models}},
author = {Byoungjoon Ahn and Robert de Mello Koch and Vatsal Garg and Antal Jevicki and Junggi Yoon},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30572},
eprint = {2610.30572},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30572},
}
RIS
TY - UNPB
TI - Beyond the Fock Vacuum in Finite-N Bilocal Algebras of Vector Models
AU - Byoungjoon Ahn
AU - Robert de Mello Koch
AU - Vatsal Garg
AU - Antal Jevicki
AU - Junggi Yoon
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.30572
UR - https://arxiv.org/abs/2610.30572
AB - We discuss the finite-N Hilbert space of bilocal operators that underlies bilocal holography of vector models, beyond the sector built on the Fock vacuum. If the microscopic oscillator Fock space carries a multiplicity-free dual action of a compact color group G and a bilocal algebra, Howe duality implies that projection to the derived subgroup [G,G] selects precisely the characters of the abelianization G^ab=G/[G,G] that occur in the Fock space. Thus O(N)/SO(N)=ℤ_2 gives two sectors, U(N)/SU(N)=U(1) gives integer determinant-charge sectors, while Sp(N) is perfect and gives no additional sector; Bose/Fermi statistics and the number of modes determine which sectors are actually realized. We construct the epsilon and determinant backgrounds that generate these sectors, together with their finite-N constraints and Casimirs, and find that the two bosonic O(N) sectors are not distinguished by any Casimir. Using group-integral projectors, we derive explicit sector-resolved characters for the O(N) and U(N) theories. Around each new background we solve the constraints with auxiliary oscillators, which form a Fermi sea for bosonic matter. In the free vector model on ℝ× S^2 the new sectors consist of baryonic primaries; we determine their energies, degeneracies and spin content exactly at finite N, together with their lowest energy at fixed angular momentum.
ER -