Integrals of motion in $W{E}_6$ CFT and the ODE/IM correspondence

Abstract

We study the ODE/IM correspondence for the ordinary differential equation associated with the affine Lie algebra $E_6^{(1)}$. The WKB expansion of the solution of the ODE is performed by the diagonalization method, and the period integrals of the WKB coefficients along the Pochhammer contour are calculated. We also compute the integrals of motion on a cylinder in two-dimensional conformal field theory with W-symmetry associated with $E_6^{(1)}$. Their eigenvalues on the highest-weight state are shown to agree with the period integrals up to the sixth order.

24 pages, 1 figure

References in corpus (7)

• Pseudo-differential equations, and the Bethe Ansatz for the classical Lie algebras
• ODE/IM correspondence and the Argyres-Douglas theory
• Wall-crossing of TBA equations and WKB periods for the third order ODE
• WKB analysis of the linear problem for modified affine Toda field equations
• Generalized Gibbs Ensemble of 2D CFTs with U(1) Charge from the AGT Correspondence
• Integrals of motion in conformal field theory with W-symmetry and the ODE/IM correspondence
• TBA equations and quantum periods for D-type Argyres-Douglas theories

Cited by in corpus (1)

• The ODE/IM Correspondence between $C(2{)}^{(2)}$-type Linear Problems and 2d $\mathcal{N}=1$ SCFT