The conformal boundary states for SU(2) at level 1

Gaberdiel, Matthias R.; Recknagel, Andreas; Watts, Gérard

doi:10.1016/s0550-3213(02)00033-0

Cited by 70 publications

(128 citation statements)

References 22 publications

(44 reference statements)

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“…As is explained in detail in [14], at the self-dual radius the structure constants are indeed given by these group theoretic expressions. We are only interested in the Virasoro symmetry here, and the different representations are therefore completely characterised by their conformal weight.…”

Section: The Factorisation Property Completeness and Remarks On Nonmentioning

confidence: 78%

“…As follows from the detailed explanation in [14], the boundary structure constants where (up to an a-independent factor) B α a is the coefficient of the Ishibashi state associated to the representation a in the boundary state labelled by α (in our case, a = (j; , m, n)), while Ξ abc is a product of the bulk OPE coefficient C abc with an element of the fusing matrix. In writing (6.2), the normalisation B α 0 = 1 for the vacuum sector has been chosen; see e.g.…”

Section: The Factorisation Property Completeness and Remarks On Nonmentioning

confidence: 99%

“…At the self-dual radius, it was shown in [14] that the most general solution to the factorisation constraint is parametrised by group elements in SL(2, C) rather than SU (2). In order to obtain the associated boundary states, one merely has to extend the representation matrix D j m,n (g) in (3.2) accordingly.…”

Section: The Factorisation Property Completeness and Remarks On Nonmentioning

confidence: 99%

See 2 more Smart Citations

Conformal boundary states for free bosons and fermions

Gaberdiel

Recknagel

2001

J. High Energy Phys.

190

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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 account for all fundamental conformal Dbranes of the free boson theory. The results can be generalised to the situation with N = 1 world-sheet supersymmetry, for which the family of boundary states interpolates between superpositions of non-BPS branes and combinations of conventional brane anti-brane pairs.

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Section: The Factorisation Property Completeness and Remarks On Nonmentioning

confidence: 78%

Section: The Factorisation Property Completeness and Remarks On Nonmentioning

confidence: 99%

Section: The Factorisation Property Completeness and Remarks On Nonmentioning

confidence: 99%

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Conformal boundary states for free bosons and fermions

Gaberdiel

Recknagel

2001

J. High Energy Phys.

190

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“…It was pointed out in [3] (and at intermediate stages of the calculations in [5]) that the boundary states can also be constructed for g ∈ SL(2, C), and in particular we can setλ = 0 to obtain the non-hermitian theory whose action S NH is in (1.4). The unitary rotation matrix (3.14) becomes a raising operator.…”

Section: Boundary Statesmentioning

confidence: 99%

Timelike boundary Liouville theory

2003

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The timelike boundary Liouville (TBL) conformal field theory consisting of a negative norm boson with an exponential boundary interaction is considered. TBL and its close cousin, a positive norm boson with a non-hermitian boundary interaction, arise in the description of the c = 1 accumulation point of c < 1 minimal models, as the worldsheet description of open string tachyon condensation in string theory and in scaling limits of superconductors with line defects. Bulk correlators are shown to be exactly soluble. In contrast, due to OPE singularities near the boundary interaction, the computation of boundary correlators is a challenging problem which we address but do not fully solve. Analytic continuation from the known correlators of spatial boundary Liouville to TBL encounters an infinite accumulation of poles and zeros. A particular contour prescription is proposed which cancels the poles against the zeros in the boundary correlator d(ω) of two operators of weight ω 2 and yields a finite result. A general relation is proposed between two-point CFT correlators and stringy Bogolubov coefficients, according to which the magnitude of d(ω) determines the rate of open string pair creation during tachyon condensation. The rate so obtained agrees at large ω with a minisuperspace analysis of previous work. It is suggested that the mathematical ambiguity arising in the prescription for analytic continuation of the correlators corresponds to the physical ambiguity in the choice of open string modes and vacua in a time dependent background. *

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“…This means that whatever mapρ is required to obtain a defect from a boundary state in the formalism of [1], the corresponding defect has zero matrix elements between 0| and |1/10 8) and so cannot be equal to either D + or D − . Gang and Yamaguchi do not give details on the precise mapρ required to obtain a defect from a boundary state in their formalism.…”

Section: Comparisons With the Results Of Gang And Yamaguchimentioning

confidence: 99%

Defects in the tri-critical Ising model

Makabe

Watts

2017

J. High Energ. Phys.

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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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The conformal boundary states for SU(2) at level 1

Cited by 70 publications

References 22 publications

Conformal boundary states for free bosons and fermions

Conformal boundary states for free bosons and fermions

Timelike boundary Liouville theory

Defects in the tri-critical Ising model

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