Integrable structure of conformal field theory, quantum KdV theory and thermodynamic Bethe ansatz

DOI10.1007/BF02101898zbMATH Open0851.35113arXivhep-th/9412229MaRDI QIDQ1918101

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Publication date: 18 November 1996

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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 ``$$-operators, act in highest weight Virasoro modules. The $$-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 $$-operators can be viewed as the continuous field theory versions of the commuting transfer-matrices of integrable lattice theory. In particular, we show that for the values $c=1-3(2n+1{)}^{2}over2n+3,n=1,2,3,\mathrm{...}$of the Virasoro central charge the eigenvalues of the $$-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 ${calM}_{2,2n+3}$; 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 $Ph{i}_{1,3}$. The relation of these $$-operators to the boundary states is also briefly described.

Full work available at URL: https://arxiv.org/abs/hep-th/9412229

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