Conformal Field Theory, Boundary Conditions and Applications to String Theory

Schweigert, Christoph; Fuchs, Juergen; Walcher, Johannes

doi:10.1142/9789812799968_0002

Cited by 21 publications

(42 citation statements)

References 38 publications

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“…Such a description of branes agrees with the general one conjectured in [30,66] for conformal field theories of the simple current extension type. The general classification of the branes proposed there, based on consistency considerations, involved equivalence classes of primary fields and characters of their "central stabilizers".…”

Section: We Infer That If the Cohomology Class [V] Is Trivial Then Ansupporting

confidence: 87%

Abelian and Non-Abelian Branes in WZW Models and Gerbes

Gawędzki

2005

Commun. Math. Phys.

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We discuss how gerbes may be used to set up a consistent Lagrangian approach to the WZW models with boundary. The approach permits to study in detail possible boundary conditions that restrict the values of the fields on the worldsheet boundary to brane submanifolds in the target group. Such submanifolds are equipped with an additional geometric structure that is summarized in the notion of a gerbe module and includes a twisted Chan-Paton gauge field. Using the geometric approach, we present a complete classification of the branes that conserve the diagonal currentalgebra symmetry in the WZW models with simple, compact but not necessarily simply connected target groups. Such symmetric branes are supported by a discrete series of conjugacy classes in the target group and may carry Abelian or non-Abelian twisted gauge fields. The latter situation occurs for the conjugacy classes with fundamental group Z 2 ×Z 2 in SO(4n)/Z 2 . The branes supported by such conjugacy classes have to be equipped with a projectively flat twisted U (2) gauge field in one of the two possible WZW models differing by discrete torsion. We show how the geometric description of branes leads to explicit formulae for the boundary partition functions and boundary operator product coefficients in the WZW models with non-simply connected target groups.

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Section: We Infer That If the Cohomology Class [V] Is Trivial Then Ansupporting

confidence: 87%

Abelian and Non-Abelian Branes in WZW Models and Gerbes

Gawędzki

2005

Commun. Math. Phys.

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“…This description of branes, obtained here from the Lagrangian considerations, agrees with the description of symmetric branes in simple current extension conformal field theories conjectured in [20] [41]. The general classification of the branes proposed there, basing on consistency considerations, involves equivalence classes of primary fields and characters of their "central stabilizers" that, for the SU (N ) WZW theory, reduce to the ordinary stabilizers Z τ in the simple current group Z.…”

Section: Groups Covered By Su(n)supporting

confidence: 81%

WZW Branes and Gerbes

2002

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We reconsider the role that bundle gerbes play in the formulation of the WZW model on closed and open surfaces. In particular, we show how an analysis of bundle gerbes on groups covered by SU (N ) permits to determine the spectrum of symmetric branes in the boundary version of the WZW model with such groups as the target. We also describe a simple relation between the open string amplitudes in the WZW models based on simply connected groups and in their simple-current orbifolds.

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“…For a careful review of the relation of CFT to string theory, see e.g. [1], especially section 6. In this paper we compare nonunitary and unitary RCFTs. We isolate in §3 what seems to be a key uncertainty in nonunitary theories: the multiplicity in the RCFT (what we will denote below mult n (o) = M oo ) of the primary o with minimal conformal weight.…”

Section: Introductionmentioning

confidence: 99%

Comments on nonunitary conformal field theories

Gannon¹

2003

Nuclear Physics B

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As is well-known, nonunitary RCFTs are distinguished from unitary ones in a number of ways, two of which are that the vacuum 0 doesn't have minimal conformal weight, and that the vacuum column of the modular S matrix isn't positive. However there is another primary field, call it o, which has minimal weight and has positive S column. We find that often there is a precise and useful relationship, which we call the Galois shuffle, between primary o and the vacuum; among other things this can explain why (like the vacuum) its multiplicity in the full RCFT should be 1. As examples we consider the minimal WSU(N) models. We conclude with some comments on fractional level admissible representations of affine algebras. As an immediate consequence of our analysis, we get the classification of an infinite family of nonunitary W 3 minimal models in the bulk.

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Conformal Field Theory, Boundary Conditions and Applications to String Theory

Cited by 21 publications

References 38 publications

Abelian and Non-Abelian Branes in WZW Models and Gerbes

Abelian and Non-Abelian Branes in WZW Models and Gerbes

WZW Branes and Gerbes

Comments on nonunitary conformal field theories

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