Exact modular S-transforms are derived for GGEs in the symplectic fermion theory, agreeing with conjectures for the W3 zero mode and mirroring free-fermion results for the KdV subset.
Pseudo-differential equations, and the Bethe Ansatz for the classical Lie algebras
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abstract
The correspondence between ordinary differential equations and Bethe ansatz equations for integrable lattice models in their continuum limits is generalised to vertex models related to classical simple Lie algebras. New families of pseudo-differential equations are proposed, and a link between specific generalised eigenvalue problems for these equations and the Bethe ansatz is deduced. The pseudo-differential operators resemble in form the Miura-transformed Lax operators studied in work on generalised KdV equations, classical W-algebras and, more recently, in the context of the geometric Langlands correspondence. Negative-dimension and boundary-condition dualities are also observed.
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The WKB periods of the E_6^(1) linear problem agree with the integrals of motion of the W E6 CFT on highest-weight states up to spin 6 under the standard parameter dictionary.
WKB periods of the fully diagonalized C(2)^{(2)} Lax operator coincide with NS-sector local IoM eigenvalues of N=1 SCFT up to sixth order under a fixed parameter dictionary.
citing papers explorer
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Modular Properties of Symplectic Fermion Generalised Gibbs Ensemble
Exact modular S-transforms are derived for GGEs in the symplectic fermion theory, agreeing with conjectures for the W3 zero mode and mirroring free-fermion results for the KdV subset.
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Integrals of motion in $WE_6$ CFT and the ODE/IM correspondence
The WKB periods of the E_6^(1) linear problem agree with the integrals of motion of the W E6 CFT on highest-weight states up to spin 6 under the standard parameter dictionary.
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The ODE/IM Correspondence between $C(2)^{(2)}$-type Linear Problems and 2d $\mathcal{N}=1$ SCFT
WKB periods of the fully diagonalized C(2)^{(2)} Lax operator coincide with NS-sector local IoM eigenvalues of N=1 SCFT up to sixth order under a fixed parameter dictionary.