Abstract:A family of conformal boundary states for a free boson on a circle is constructed. The family contains superpositions of conventional U(1)-preserving Neumann and Dirichlet branes, but for general parameter values the boundary states are fundamental and preserve only the conformal symmetry. The relative overlaps satisfy Cardy's condition, and each boundary state obeys the factorisation constraint.It is also argued that, together with the conventional Neumann and Dirichlet branes, these boundary states already a… Show more
“…Our analysis implies in particular that for this theory the usual Neumann and Dirichlet branes already account for all N = 2 D-branes. This is in marked contrast to the results in the non-supersymmetric case, or the case with N = 1 supersymmetry, where there exist conformal or N = 1 superconformal D-branes that do not have an interpretation in terms of Neumann or Dirichlet branes [4].…”
The most general N = 2 superconformal boundary states for the c = 3 theory consisting of two (uncompactified) free bosons and fermions are constructed. It is shown that the only N = 2 boundary states are the familiar Dirichlet boundary states, as well as the Neumann boundary states with an arbitrary electric field.
“…Our analysis implies in particular that for this theory the usual Neumann and Dirichlet branes already account for all N = 2 D-branes. This is in marked contrast to the results in the non-supersymmetric case, or the case with N = 1 supersymmetry, where there exist conformal or N = 1 superconformal D-branes that do not have an interpretation in terms of Neumann or Dirichlet branes [4].…”
The most general N = 2 superconformal boundary states for the c = 3 theory consisting of two (uncompactified) free bosons and fermions are constructed. It is shown that the only N = 2 boundary states are the familiar Dirichlet boundary states, as well as the Neumann boundary states with an arbitrary electric field.
The c = 1 Liouville theory has received some attention recently as the Euclidean version of an exact rolling tachyon background. In an earlier paper it was shown that the bulk theory can be identified with the interacting c = 1 limit of unitary minimal models. Here we extend the analysis of the c = 1-limit to the boundary problem. Most importantly, we show that the FZZT branes of Liouville theory give rise to a new 1-parameter family of boundary theories at c = 1. These models share many features with the boundary Sine-Gordon theory, in particular they possess an open string spectrum with band-gaps of finite width. We propose explicit formulas for the boundary 2-point function and for the bulk-boundary operator product expansion in the c = 1 boundary Liouville model. As a by-product of our analysis we also provide a nice geometric interpretation for ZZ branes and their relation with FZZT branes in the c = 1 theory.
SPhT-T04/121hep-th/0409256 IHES/P/04/42
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.
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