Supersymmetry in the Boundary Tricritical Ising Field Theory

Abstract

We argue that it is possible to maintain both supersymmetry and integrability in the boundary tricritical Ising field theory. Indeed, we find two sets of boundary conditions and corresponding boundary perturbations which are both supersymmetric and integrable. The first set corresponds to a "direct sum" of two non-supersymmetric theories studied earlier by Chim. The second set corresponds to a one-parameter deformation of another theory studied by Chim. For both cases, the conserved supersymmetry charges are linear combinations of Q,Q and the spin-reversal operator Γ.

TBA boundary flows in the tricritical Ising field theory

“…We shall refer to this field theory as the "tricritical Ising model " or TIM for short. The bulk S matrix was proposed in [7], and boundary S matrices were proposed in [8,9]. This field theory has several notable properties, which render it a very attractive toy model: it is unitary; it is supersymmetric; and it is one of the simplest examples of a model of massive kinks, whose scattering matrices are of RSOS [10,11] type.…”

“…One of the principal aims of this paper is to perform an analogous TBA check of the boundary S matrices which have been proposed in [8,9]. Such an analysis is technically nontrivial, since neither the bulk nor boundary S matrices are diagonal.…”

“…Let us recall [22,8,9] that the tricritical Ising CFT has a discrete set of (super) conformal boundary conditions. Boundary perturbations can lead to flows among these boundary conditions [8,31,32,33,34,9]. A TBA description of the nonsupersymmetric flows was proposed in [31] on the basis of an analogy with the Kondo problem.…”

Errata: Supersymmetry in the Boundary Tricritical Ising Field Theory

“…(5.4) in Ref. 1, we see that the first two lines are the same, but the third line is different. The boundary S matrix (5.10) satisfies all of these constraints.…”

“…As in Ref. 1, we assume that the supersymmetry operators Q andQ and the spin-reversal operator Γ act on the boundary operator for the ground state as follows,…”