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Differential equations and integrable models: the SU(3) case

Patrick Dorey·Roberto Tateo
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Abstract

We exhibit a relationship between the massless $a_2^{(2)}$ integrable quantum field theory and a certain third-order ordinary differential equation, thereby extending a recent result connecting the massless sine-Gordon model to the Schrödinger equation. This forms part of a more general correspondence involving $A_2$-related Bethe ansatz systems and third-order differential equations. A non-linear integral equation for the generalised spectral problem is derived, and some numerical checks are performed. Duality properties are discussed, and a simple variant of the nonlinear equation is suggested as a candidate to describe the finite volume ground state energies of minimal conformal field theories perturbed by the operators $ϕ_{12}$, $ϕ_{21}$ and $ϕ_{15}$. This is checked against previous results obtained using the thermodynamic Bethe ansatz.

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Patrick Dorey, Roberto Tateo. 2000-02-07. Differential equations and integrable models: the SU(3) case. https://doi.org/10.1016/s0550-3213(99)00791-9

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