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arXiv:hep-th/0308075 · Nuclear Physics B

Exact ϕ1,3 boundary flows in the tricritical Ising model

Giovanni Feverati, Paul A. Pearce, Francesco Ravanini

Published Oct 27, 2003• 19 citations
arXivHTMLPDF
DOI
10.1016/j.nuclphysb.2003.09.059

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We show how a lattice approach can be used to derive Thermodynamic Bethe Ansatz (TBA) equations describing all excitations for boundary flows. The method is illustrated for a prototypical flow of the tricritical Ising model by considering the continuum scaling limit of the A4 lattice model with integrable boundaries. Fixing the bulk weights to their critical values, the integrable boundary weights admit two boundary fields ξ and η which play the role of the perturbing boundary fields ϕ1,3 and ϕ1,2 inducing the renormalization group flow between boundary fixed points. The excitations are completely classified in terms of (m,n) systems and quantum numbers but the string content changes by certain mechanisms along the flow. For our prototypical example, we identify these mechanisms and the induced map between the relevant finitized Virasoro characters. We also solve the boundary TBA equations numerically to determine the flows for the leading excitations.

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The integrable perturbation of the degenerate boundary condition ( d ) by the φ 1,3 boundary field generates a renormalization group flow down to the superposition of Cardy boundary states (+)&(−). Exact thermodynamic Bethe ansatz (TBA) equations for all the excited states are derived here extending the results of Feverati et al (2003 Nucl. Phys. B 675 469) to this case. As an intermediate step, the non-Cardy boundary conformal sector (+)&(−) is also described as the scaling limit of an A 4 lattice model with appropriate integrable boundary conditions and produces the first example of superposition of finitized Virasoro characters.
We show how a lattice approach can be used to derive Thermodynamic Bethe Ansatz (TBA) equations describing all excitations for boundary flows. The method is illustrated for a prototypical flow of the tricritical Ising model by considering the continuum scaling limit of the A4 lattice model with integrable boundaries. Fixing the bulk weights to their critical values, the integrable boundary weights admit two boundary fields ξ and η which play the role of the perturbing boundary fields ϕ1,3 and ϕ1,2 inducing the renormalization group flow between boundary fixed points. The excitations are completely classified in terms of (m,n) systems and quantum numbers but the string content changes by certain mechanisms along the flow. For our prototypical example, we identify these mechanisms and the induced map between the relevant finitized Virasoro characters. We also solve the boundary TBA equations numerically to determine the flows for the leading excitations.