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.
Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz
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abstract
We construct the quantum versions of the monodromy matrices of KdV theory. The traces of these quantum monodromy matrices, which will be called as ``${\bf T}$-operators'', act in highest weight Virasoro modules. The ${\bf T}$-operators depend on the spectral parameter $\lambda$ and their expansion around $\lambda = \infty$ generates an infinite set of commuting Hamiltonians of the quantum KdV system. The ${\bf T}$-operators can be viewed as the continuous field theory versions of the commuting transfer-matrices of integrable lattice theory. In particular, we show that for the values $c=1-3{{(2n+1)^2}\over {2n+3}} , n=1,2,3,... $of the Virasoro central charge the eigenvalues of the ${\bf T}$-operators satisfy a closed system of functional equations sufficient for determining the spectrum. For the ground-state eigenvalue these functional equations are equivalent to those of massless Thermodynamic Bethe Ansatz for the minimal conformal field theory ${\cal M}_{2,2n+3}$; in general they provide a way to generalize the technique of Thermodynamic Bethe Ansatz to the excited states. We discuss a generalization of our approach to the cases of massive field theories obtained by perturbing these Conformal Field Theories with the operator $\Phi_{1,3}$. The relation of these ${\bf T}$-operators to the boundary states is also briefly described.
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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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