English

Regge trajectories from the adjoint sector of Matrix Quantum Mechanics

High Energy Physics - Theory 2026-04-14 v2

Abstract

We reexamine the large NN limit of SU(N)(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 Δ2n/α\Delta^2 \sim n/ \alpha'. 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.

Keywords

Cite

@article{arxiv.2603.04522,
  title  = {Regge trajectories from the adjoint sector of Matrix Quantum Mechanics},
  author = {Igor R. Klebanov and Henry W. Lin and Pavel Meshcheriakov},
  journal= {arXiv preprint arXiv:2603.04522},
  year   = {2026}
}

Comments

21 pages, 4 figures; v2: added refs and fixed typos