Anharmonic Oscillators, Spectral Determinant and Short Exact Sequence of affine U_q(sl_2)

TL;DR

This paper proves a conjecture linking the spectral determinant of anharmonic oscillators with vacuum eigenvalues in transfer matrices, utilizing the exact sequence of quantum affine algebra U_q(sl_2).

Contribution

It establishes a rigorous proof of a conjecture connecting spectral theory and quantum algebra representations, highlighting the role of the exact sequence of U_q(sl_2).

Findings

Confirmed the conjecture relating spectral determinants and transfer matrix eigenvalues.

Demonstrated the importance of the exact sequence of U_q(sl_2) in the proof.

Bridged concepts in spectral theory, quantum groups, and statistical mechanics.

Abstract

We prove one of conjectures, raised by Dorey and Tateo in the connection among the spectral determinant of anharmonic oscillator and vacuum eigenvalues of transfer matrices in field theory and statistical mechanics. The exact sequence of $U_q(\hat{sl}_2)$ plays a fundamental role in the proof.