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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.04522 |
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Table of Contents:
- We reexamine the large $N$ limit of SU$(N)$ symmetric quantum mechanics of a Hermitian matrix whose singlet sector is well known to be exactly solvable via free fermions. When the Fermi level approaches a maximum of the potential, there is critical behavior corresponding to string theory in two dimensions. We uncover new phenomena in the adjoint sector by solving the Marchesini-Onofri equation both numerically and analytically using semiclassical approximations: at criticality, the spectrum is governed by Regge trajectories with energy eigenvalues growing according to $Δ^2 \sim n/ α'$. In the dual 2D string theory, we interpret these states as oscillatory excitations of a ``short'' folded open string. Up to sub-leading corrections, this Regge behavior is essentially universal and is insensitive to the particular potential we choose to approach criticality. Slightly away from criticality, the highly excited states transition into ``long strings'' that extend far into the Liouville direction.