Boundary S Matrix for the Tricritical Ising Model

We show how a large class of boundary RG flows in two-dimensional conformal field theories can be summarized in a single rule. This rule is a generalization of the 'absorption of the boundary spin'-principle of Affleck and Ludwig and applies to all theories which have a description as a coset model. We give a formulation for coset models with arbitrary modular invariant partition function and present evidence for the conjectured rule. The second half of the article contains an illustrated section of examples where the rule is applied to unitary minimal models of the A-and D-series, in particular the 3-state Potts model, and to parafermion theories. We demonstrate how the rule can be used to compute brane charge groups in the example of N = 2 minimal models.

Section: Tricritical Ising Modelmentioning

confidence: 70%

Organizing boundary RG flows

Fredenhagen

2003

“…A CBC is also characterized by the so-called boundary entropy or ground-state degeneracy (g) factor [11], which (roughly speaking) is a measure of the number of bulk vacua which are compatible with a given CBC. This is well illustrated in the unitary minimal models [9], [12]. As can be seen from (1.2), the boundary CFT in general has perturbations by both bulk (Φ (∆ ,∆) ) and boundary (Φ (∆) ) relevant primary fields.…”

Section: Introductionmentioning

confidence: 77%

“…Moreover, we consider 12) where the boundary scale θ B is finite. For the sign − in the limit (2.11), the boundary S matrix reduces to S(θ − θ B ) −1 [14], and we obtain…”

Section: Boundarymentioning

confidence: 99%

“…By analogy with the bulk SYL model, as well as with the boundary YL model, we expect that the boundary S matrix of the boundary SYL model should be some reduction of that of the boundary supersymmetric sine-Gordon model [45], or equivalently, the boundary supersymmetric sinh-Gordon model [15]. We therefore consider 12) where the scalar factor S Y L (θ ; b) is given by (2.3), and S SU SY (θ ; φ) is given by…”

Section: Boundary S Matrixmentioning

confidence: 99%

See 1 more Smart Citation

The scaling supersymmetric Yang–Lee model with boundary

Ahn¹,

Nepomechie²

2001

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.

“…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.…”

Section: Introductionmentioning

confidence: 99%

TBA boundary flows in the tricritical Ising field theory

Nepomechie

Ahn

2002

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.