Klein bottles and simple currents

Huiszoon, L.R.; Schellekens, A.N.; Sousa, Nuno

doi:10.1016/s0370-2693(99)01241-1

Cited by 49 publications

(71 citation statements)

References 16 publications

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“…These results admit interesting generalizations to cases where boundaries and crosscaps preserve only part of the bulk symmetry [171], that correspond to allowing (discrete) deformations of the types described in the previous section in the geometries underlying these rational constructions.…”

Section: Boundary Conformal Field Theory Orientifolds and Branesmentioning

confidence: 61%

Erratum to “Open strings”

2003

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Abstract. This review is devoted to open strings, and in particular to the often surprising features of their spectra. It follows and summarizes developments that took place mainly at the University of Rome "Tor Vergata" over the last decade, and centred on world-sheet aspects of the constructions now commonly referred to as "orientifolds". Our presentation aims to bridge the gap between the world-sheet analysis, that first exhibited many of the novel features of these systems, and their geometric description in terms of extended objects, D-branes and O-planes, contributed by many other colleagues, and most notably by J. Polchinski. We therefore proceed through a number of prototype examples, starting from the bosonic string and moving on to tendimensional fermionic strings and their toroidal and orbifold compactifications, in an attempt to guide the reader in a self-contained journey to the more recent developments related to the breaking of supersymmetry.

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Section: Boundary Conformal Field Theory Orientifolds and Branesmentioning

confidence: 61%

Erratum to “Open strings”

2003

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“…The main tool in this approach was the use of sewing and modular duality constraints in order to find consistent expressions for the crosscap states encoding the action of the orientation inversion in the closed string sector. The algebraic approach was further developed in the context of more general orientifolds combining simple-current orbifolds and orientation reversal in [17,18,16,9,5]. It gave rise to an abstract formulation of the relevant topological structures in the language of tensor categories [29].…”

Section: Introductionmentioning

confidence: 99%

WZW Orientifolds and Finite Group Cohomology

Gawędzki

Suszek

Waldorf

2008

Commun. Math. Phys.

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The simplest orientifolds of the WZW models are obtained by gauging a Z 2 symmetry group generated by a combined involution of the target Lie group G and of the worldsheet. The action of the involution on the target is by a twisted inversion g → (ζg) −1 , where ζ is an element of the center of G. It reverses the sign of the KalbRamond torsion field H given by a bi-invariant closed 3-form on G. The action on the worldsheet reverses its orientation. An unambiguous definition of Feynman amplitudes of the orientifold theory requires a choice of a gerbe with curvature H on the target group G, together with a so-called Jandl structure introduced in [31]. More generally, one may gauge orientifold symmetry groups Γ = Z 2 ⋉Z that combine the Z 2 -action described above with the target symmetry induced by a subgroup Z of the center of G. To define the orientifold theory in such a situation, one needs a gerbe on G with a Z-equivariant Jandl structure. We reduce the study of the existence of such structures and of their inequivalent choices to a problem in group-Γ cohomology that we solve for all simple simply-connected compact Lie groups G and all orientifold groups Γ = Z 2 ⋉Z.

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“…20) which is plausible since the action is entirely on the space of Ishibashi states. Then we can derive…”

Section: This Leads To the Following Expressionmentioning

confidence: 99%

Orientation matters for NIMreps

Sousa¹,

Schellekens²

2003

Nuclear Physics B

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The problem of finding boundary states in CFT, often rephrased in terms of "NIMreps" of the fusion algebra, has a natural extension to CFT on non-orientable surfaces.This provides extra information that turns out to be quite useful to give the proper interpretation to a NIMrep. We illustrate this with several examples. This includes a rather detailed discussion of the interesting case of the simple current extension of A 2 level 9, which is already known to have a rich structure. This structure can be disentangled completely using orientation information. In particular we find here and in other cases examples of diagonal modular invariants that do not admit a NIMrep, suggesting that there does not exist a corresponding CFT. We obtain the complete set of NIMreps (plus Moebius and Klein bottle coefficients) for many exceptional modular invariants of WZW models, and find an explanation for the occurrence of more than one NIMrep in certain cases. We also (re)consider the underlying formalism, emphasizing the distinction between oriented and unoriented string annulus amplitudes, and the origin of orientation-dependent degeneracy matrices in the latter.

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Klein bottles and simple currents

Cited by 49 publications

References 16 publications

Erratum to “Open strings”

Erratum to “Open strings”

WZW Orientifolds and Finite Group Cohomology

Orientation matters for NIMreps

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