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

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

1999-10-13

arxiv.org/abs/hep-th/9910102v3

Nucl.Phys. B571 (2000) 583-606; Erratum-ibid. B603 (2001) 582

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, Latex 2e, 3 figures, uses graphics, cite. v2: Typos corrected, section 6 expanded and an error fixed,references adde

Scientific paper

10.1016/S0550-3213(99)00791-9

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 Schr\"odinger 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 $\phi_{12}$, $\phi_{21}$ and $\phi_{15}$. This is checked against previous results obtained using the thermodynamic Bethe ansatz.

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