The Nonlocal Involutive Charges of the CFT ${\cal M}_{3,4}$

TL;DR

This paper explores the spectral properties of nonlocal involutive charges in the minimal conformal field theory ${ m M}_{3,4}$ with central charge 1/2, proposing analytic formulas and connecting them to spectral zeta functions of Schrödinger Hamiltonians.

Contribution

It introduces explicit analytic formulas for the eigenvalues of nonlocal involutive charges and relates them to spectral zeta functions, advancing understanding of integrable structures in this CFT.

Findings

Proposed analytic formulas for eigenvalues of nonlocal involutive charges.

Established connection between eigenvalues and spectral zeta functions.

Derived an exact formula for the $ ext{ extPsi}$ function at $c=1/2$.

Abstract

We consider continuum minimal ${\cal M}_{3,4} $ with central charge $c=1/2$. The eigenvalues of the known local involutive charges are known to be related to spectral zeta functions of suitable one dimensional shroedinger hamiltonians. We investigate this connection. We Propose analytic formulae for the eigenvalues of Nonlocal Involutive Charges. We also propose an exact formula for the eigenvalues of the $\Psi$ function of BLZ at central charge $c=1/2$ which reduces to the local non local and dual non local involutive charges for special values on the imaginary axis.