WZW Orientifolds and Finite Group Cohomology

Gawędzki, Krzysztof; Suszek, Rafał R.; Waldorf, Konrad

doi:10.1007/s00220-008-0525-2

Cited by 15 publications

(36 citation statements)

References 33 publications

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“…where we follow the conventions of [GSW1]. One verifies that D (r+1) Iff 1 = (f, φ) andf 2 = (f, φ) are twoČech-extended maps that differ only in the choice of the index map, the resulting pullback gerbes are stably isomorphic.…”

Section: Holonomy For World-sheets With Defect Networkmentioning

confidence: 93%

Gerbe-holonomy for surfaces with defect networks

Runkel¹,

Suszek²

2009

Advances in Theoretical and Mathematical Physics

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We define the sigma-model action for world-sheets with embedded defect networks in the presence of a three-form field strength. We derive the defect gluing condition for the sigma-model fields and their derivatives, and use it to distinguish between conformal and topological defects. As an example, we treat the WZW model with defects labelled by elements of the centre Z(G) of the target Lie group G; comparing the holonomy for different defect networks gives rise to a 3-cocycle on Z(G). Next, we describe the factorisation properties of two-dimensional quantum field theories in the presence of defects and compare the correlators for different defect networks in the quantum WZW model. This, again, results in a 3-cocycle on Z(G). We observe that the cocycles obtained in the classical and in the quantum computation are cohomologous. *

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Section: Holonomy For World-sheets With Defect Networkmentioning

confidence: 93%

Gerbe-holonomy for surfaces with defect networks

Runkel¹,

Suszek²

2009

Advances in Theoretical and Mathematical Physics

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“…Accordingly, we obtain This applies to the case, studied in [26,27], of Γ-equivariant structures on the WZW gerbe G k overG for Γ = Z ⊂Z acting onG by multiplication.…”

Section: A Obstructions To 1-isomorphisms αmentioning

confidence: 97%

“…For the bundle isomorphism α to define a gerbe 1-isomorphism from (G k ) 12 to I ρ k ⊗ (G k ) 2 , one has to require a proper behavior with respect to the groupoid multiplication [26]. More precisely, what is needed is the coincidence of two composed isomorphisms of line bundles over W [3] 12 .…”

Section: A Wzw Gerbes Over Compact Simply Connected Simple Lie Groupsmentioning

confidence: 99%

“…For the line bundle isomorphism β to provide a gerbe 2-isomorphism required by Definition 5.1, one needs (see [26]) that over W [2] 123 ∼ = (G 2 × Y [6] )/Z 2 , (7.73) with the action ofZ 2 induced from that in (7.62), the diagram of line bundle isomorphisms with the exterior subscripts referring to the pullbacks to W [2] 123 and with the obvious pullbacks omitted, be commutative. This is checked in Appendix 8.…”

Section: A Wzw Gerbes Over Compact Simply Connected Simple Lie Groupsmentioning

confidence: 99%

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Global Gauge Anomalies in Two-Dimensional Bosonic Sigma Models

Gawędzki

Suszek

Waldorf

2010

Commun. Math. Phys.

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Abstract:We revisit the gauging of rigid symmetries in two-dimensional bosonic sigma models with a Wess-Zumino term in the action. Such a term is related to a background closed 3-form H on the target space. More exactly, the sigma-model Feynman amplitudes of classical fields are associated to a bundle gerbe with connection of curvature H over the target space. Under conditions that were unraveled more than twenty years ago, the classical amplitudes may be coupled to the topologically trivial gauge fields of the symmetry group in a way which assures infinitesimal gauge invariance. We show that the resulting gauged Wess-Zumino amplitudes may, nevertheless, exhibit global gauge anomalies that we fully classify. The general results are illustrated on the example of the WZW and the coset models of conformal field theory. The latter are shown to be inconsistent in the presence of global anomalies. We introduce a notion of equivariant gerbes that allow an anomaly-free coupling of the Wess-Zumino amplitudes to all gauge fields, including the ones in non-trivial principal bundles. Obstructions to the existence of equivariant gerbes and their classification are discussed. The choice of different equivariant structures on the same bundle gerbe gives rise to a new type of discrete-torsion ambiguities in the gauged amplitudes. An explicit construction of gerbes equivariant with respect to the adjoint symmetries over compact simply connected simple Lie groups is given.

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“…We further specialize to the case where the orientifold involution is a group automorphism. While this is not the only possibility, and other literature on WZW orientifolds (for example, ) deals with the case of group anti‐automorphisms (or twists thereof), the automorphism case certainly seems like a natural case to consider, and it could be that orientifold theories on a group

G

with a group involution

ι

and

G^{ι} = H

are related to ‘coset theories’ on

G / H

.…”

Section: Orientifold Dualities For Lie Groups With Involutionmentioning

confidence: 99%

Group dualities, T‐dualities, and twisted K‐theory

Mathai

Rosenberg

2017

J. London Math. Soc.

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Abstract. This paper explores further the connection between Langlands duality and T-duality for compact simple Lie groups, which appeared in work of Daenzer-Van Erp and Bunke-Nikolaus. We show that Langlands duality gives rise to isomorphisms of twisted K-groups, but that these K-groups are trivial except in the simplest case of SU(2) and SO(3). Along the way we compute explicitly the map on H 3 induced by a covering of compact simple Lie groups, which is either 1 or 2 depending in a complicated way on the type of the groups involved. We also give a new method for computing twisted K-theory using the Segal spectral sequence, which is better adapted to many problems involving compact groups. Finally we study a duality for orientifolds based on complex Lie groups with an involution.

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WZW Orientifolds and Finite Group Cohomology

Cited by 15 publications

References 33 publications

Gerbe-holonomy for surfaces with defect networks

Gerbe-holonomy for surfaces with defect networks

Global Gauge Anomalies in Two-Dimensional Bosonic Sigma Models

Group dualities, T‐dualities, and twisted K‐theory

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