The scaling supersymmetric Yang–Lee model with boundary

Abstract

We define the scaling supersymmetric Yang-Lee model with boundary as the (1 , 3) perturbation of the superconformal minimal model SM(2/8) (or equivalently, the (1 , 5) perturbation of the conformal minimal model M(3/8)) with a certain conformal boundary condition. We propose the corresponding boundary S matrix, which is not diagonal for general values of the boundary parameter. We argue that the model has an integral of motion corresponding to an unbroken supersymmetry, and that the proposed S matrix commutes with a similar quantity. We also show by means of a boundary TBA analysis that the proposed boundary S matrix is consistent with massless flow away from the ultraviolet conformal boundary condition.

Thermodynamics and conformal properties of XXZ chains with alternating spins

“…In a previous work [26] the boundary free energy for the alternating chain was computed by means of the thermodynamic Bethe ansatz method. On the other hand, the effective central charge of the open XXZ spin chain with general diagonal and non-diagonal boundaries was computed recently by means of finite size corrections [48]. A similar computation, but for diagonal boundaries only, was also undertaken in [49].…”

“…(48) for several alternating chains and computed the corresponding ground state energy. Then we used formula (71) and eq.…”

Exact solution of the supersymmetric sinh-Gordon model with boundary

“…These models have bulk and boundary S matrices which are similar to those of SShG, and therefore, we expect similar inversion identities to hold. We hope to report on these models in the near future [56]. Finally, we recall [46] that one can readily obtain the Hamiltonian of an integrable open quantum spin chain with N spins from any homogeneous open-chain transfer matrix t(θ|0) (4.1).…”

Supersymmetry in the Boundary Tricritical Ising Field Theory

“…Motivated by the plausibility argument given above that the boundary TIM (4.1) has a conserved supersymmetry charge (4.4) and by the observation that the boundary perturbation breaks spin-reversal symmetry (see also [15], [16]), we consider the following operator…”

“…Although the question of whether supersymmetry can be maintained in the boundary theory was raised in the seminal work of Chim [7], it has not been addressed until now. 1 We have recently investigated the issue of integrability and supersymmetry in the presence of a boundary for other models: the scaling supersymmetric Yang-Lee model [15], and the N = 1 and N = 2 sine-Gordon models [16]. However, in contrast to those models whose particles have vertex-type scattering matrices, the tricritical Ising field theory contains kinks which have RSOS-type scattering matrices.…”