Defects in the tri-critical Ising model

Abstract

Abstract:We consider two different conformal field theories with central charge c = 7/10. One is the diagonal invariant minimal model in which all fields have integer spins; the other is the local fermionic theory with superconformal symmetry in which fields can have halfinteger spin. We construct new conformal (but not topological or factorised) defects in the minimal model. We do this by first constructing defects in the fermionic model as boundary conditions in a fermionic theory of central charge c = 7/5, using the folding trick as first proposed by Gang and Yamaguchi [1]. We then act on these with interface defects to find the new conformal defects. As part of the construction, we find the topological defects in the fermionic theory and the interfaces between the fermionic theory and the minimal model. We also consider the simpler case of defects in the theory of a single free fermion and interface defects between the Ising model and a single fermion as a prelude to calculations in the tri-critical Ising model.

The reflection coefficient for minimal model conformal defects from perturbation theory

“…This model has h = 3/5, y = 2/5 and is again far from the perturbative regime but we can at least compare the perturbative calculation with the values of R found in [7]. We can also calculate the value of the defect entropy, g, of the perturbative defect and of the exact defects as a guide to how reliable the perturbative calculation is this far from the small y regime.…”

“…Non-topological non-factorising defects were constructed for this model in [7]. The defects found in [7] are still rather special, and are likely to be sums of more fundamental non-topological non-factorising defects of the same value of R.…”

“…. This can be compared with the two distinct values of R for non-topological non-factorised defects found in [7], which are…”

“…We know that none of the defects found in [7] can be equal to C since they all have g greater than 2. If there is a direct relation, then the most likely explanation is that the defects in [7] are composite defects formed of two [or more] defects with the same values of R.…”

“…The conformal defects in the Ising model were classified in [5] (and in the much simpler Lee-Yang model in [2]), but in general the only results found are either perturbative or numerical [6]. More recently, we have also found exact expressions for conformal defects in the tricritical Ising model [7] (based on ideas in [8]). …”