Spectral determinants for Schroedinger equation and Q-operators of Conformal Field Theory
V. Bazhanov, S. Lukyanov, A. Zamolodchikov
TL;DR
This paper proves a conjecture linking the vacuum eigenvalues of CFT Q-operators to spectral determinants of a modified one-dimensional Schrödinger operator across all parameter values, extending previous special case results.
Contribution
It establishes a general proof of the relation between CFT Q-operators and spectral determinants, generalizing previous special case findings.
Findings
Confirmed the conjecture for all parameter values
Established a modified Schrödinger operator framework
Extended the relation beyond special parameter cases
Abstract
Relation between the vacuum eigenvalues of CFT Q-operators and spectral determinants of one-dimensional Schroedinger operator with homogeneous potential, recently conjectured by Dorey and Tateo for special value of Virasoro vacuum parameter p, is proven to hold, with suitable modification of the Schroedinger operator, for all values of p.
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