Quantizing the folded string in AdS${}_2$

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 $g\equiv \frac{(R_{\text{AdS}}{)}^2}{2\pi {\alpha }^{\mathrm{\prime }}}$ 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.