Quantizing the folded string in AdS$_2$

TL;DR

This paper introduces a novel quantization approach for folded strings in AdS$_2$, revealing a spectrum that aligns with fermionic operators in the SYK model, thus bridging string theory and quantum many-body physics.

Contribution

It develops an alternative quantization method for folded strings in AdS$_2$ using integrability-inspired variables and boundary conditions, matching SYK model spectra.

Findings

Spectrum matches fermion bilinear operators in SYK model

Uses integrability-inspired variables for quantization

Boundary conditions yield exact spectral correspondence

Abstract

In two-dimensional flat space, the oscillatory motion of a closed folded string--or alternatively, two massless particles connected by a string--can be quantized using the 't Hooft equation. This paper presents an alternative method for quantizing the folded string in anti-de Sitter space. By using variables inspired by integrability, setting $g \equiv {(R_\text{AdS})^2 \over 2\pi \alpha'}$ to a specific p-dependent $\mathcal{O}(1)$ value, and applying a particular boundary condition to the antisymmetrized wavefunction, we obtain a spectrum that precisely matches that of fermion bilinear operators in the disorder-averaged Sachdev-Ye-Kitaev model with p-fermion interactions.