TBA boundary flows in the tricritical Ising field theory

Abstract

Boundary S matrices for the boundary tricritical Ising field theory (TIM), both with and without supersymmetry, have previously been proposed. Here we provide support for these S matrices by showing that the corresponding boundary entropies are consistent with the expected boundary flows. We develop the fusion procedure for boundary RSOS models, with which we derive exact inversion identities for the TIM. We confirm the TBA description of nonsupersymmetric boundary flows of Lesage et al., and we obtain corresponding descriptions of supersymmetric boundary flows.

Quench dynamics in two-dimensional integrable SUSY models

“…Therefore also in this case it is very useful to compare the boundary states identified by the SUSY equations with those already discussed in the literature. As we are going to show, the two classes of boundary states with zero topological charge, defined through (Q + ± iQ − ) |B = 0 are in one to one correspondence with the SUSY spatial boundary conditions of the TIM studied by Nepomechie in [46] and there denoted as Ramond (R) and Neveu-Schwartz (NS) boundary conditions. This terminology comes from the general classification of the Conformal Boundary States that the Tricritical Ising Model can have: since this model has six primary operators under the Virasoro algebra, according to the analysis of Cardy [48], there could be six possible conformal invariant boundary states.…”

“…Comparison with known boundary solutions. The Tricritical Ising Model with boundary has been studied in detail in a series of papers, both at and away from criticality [45][46][47][48]. Therefore also in this case it is very useful to compare the boundary states identified by the SUSY equations with those already discussed in the literature.…”

“…The parameter r is related to the boundary g-factors (see the papers [45][46][47]) for detail) while the parameter ζ is related to a boundary coupling: this parameter rules the energies of the excited states on the boundary, related by e 0 = e ± + cos ζ .…”

Moduli space coordinates and excited state g-functions

“…We find formulae for these overlaps using the known thermodynamic Bethe Ansatz descriptions of the ground and first excited state on the cylinder and show that they give a global coordinate on the space of boundary conditions, showing it is smooth and compact as expected. * Email: gerard.watts@kcl.ac.uk 1 It should be noted that the actual equations for the g-functions of the bulk off-critical flows in this paper are not correct, but exactly at the bulk critical point they do correctly reproduce the sequence of boundary flows 2 The g-functions derived in [15] are only correct for the purely boundary flows; when bulk perturbations are included they suffer from the same problems described in [11]…”

A note on the IR limit of the NLIEs of boundary supersymmetric sine-Gordon model

“…Indeed (4.9) is a reflection factor of the boundary tricritical Ising model [58]- [60], the integral representation of which is given in [61]. This is the RSOS factor.…”