The Gauging of Two-Dimensional Bosonic Sigma Models on World-Sheets With Defects

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

doi:10.1142/s0129055x13500104

Cited by 5 publications

(8 citation statements)

References 67 publications

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“…As was observed in [11], it is possible, however, that the gauged action exhibits global gauge anomalies that lead to its non-invariance under some "large" local gauge transformations non-homotopic to unity. The phenomenon was analyzed in detail for sigma models on closed worldsheets in [11] and on worldsheets with boundaries and defects in [12]. In the case of Wess-Zumino-Witten (WZW) models of conformal field theory with Lie group G =G/Z as the target, whereG is the universal covering group of G and Z is a subgroup of the centerZ ofG, with the Wess-Zumino term corresponding to the bi-invariant closed 3-form H k = k 12π tr(g −1 dg) 3 , the local gauge anomalies are absent for a restricted class of rigid symmetries.…”

Section: Introductionmentioning

confidence: 99%

Global Gauge Anomalies in Coset Models of Conformal Field Theory

Fromont¹,

Gawędzki

Tauber

2014

Commun. Math. Phys.

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We study the occurrence of global gauge anomalies in the coset models of two-dimensional conformal field theory that are based on gauged WZW models. A complete classification of the non-anomalous theories for a wide family of gauged rigid adjoint or twisted-adjoint symmetries of WZW models is achieved with the help of Dynkin's classification of Lie subalgebras of simple Lie algebras.Considering each subgroup Z and the corresponding values of a 1 , a 2 ,ã 1 , andã 2 , and recalling the admissible values (3.33) of the level, we deduce Proposition 3.10 The twisted coset models corresponding to Lie algebra g = so(8), outer automorphism ω 4 and arbitrary subalgebra do not have anomalies for Z =Z (+ theory) and Z = Z 1 , Z 2 or Z diag . The models with h = g and Z =Z (-theory) is anomalous.The results for the twist ω −1 4 may be deduced from the above proposition if we observe that ω −1 4 may be obtained from ω 4 by the conjugation by any cyclic outer automorphism ω ′ of order 2. Hence the conditions for the absence or the presence of anomalies for the theory twisted by ω −1 4 are as for the ones for the twist ω 4 except for the exchange of the ± theories for Z =Z and k odd leading to Proposition 3.11 The twisted coset models corresponding to Lie algebra g = so(8), outer automorphism ω −1 4 and arbitrary subalgebra do not have anomalies for Z =Z ((−) k theory) and Z = Z 1 , Z 2 or Z diag . The models with h = g, and Z =Z ((−) k+1 theory) is anomalous.This may be confirmed by a direct calculation. 9

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Section: Introductionmentioning

confidence: 99%

Global Gauge Anomalies in Coset Models of Conformal Field Theory

Fromont¹,

Gawędzki

Tauber

2014

Commun. Math. Phys.

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“…If Σ 2 is a closed oriented surface, then any gerbe connection on Σ 2 is isomorphic to I B for some B ∈ Ω 2 (Σ 2 ). The holonomy is defined by Therefore, one can consider the equivariant holonomy of objects in G-Grb ∇ (M ) as a way to define WZW terms in gauged sigma models [Wit,FOS,GSW1,GSW2,BE].…”

Section: Applicationsmentioning

confidence: 99%

“…Therefore, one can consider the equivariant holonomy of objects in G-Grb ∇ (M ) as a way to define WZW terms in gauged sigma models [Wit,FOS,GSW1,GSW2,BE].…”

Section: Applicationsmentioning

confidence: 99%

“…The tools developed in this paper should aid especially in answering existence/uniqueness questions and in better developing functorial constructions. In particular, the formal properties of Grb ∇ (E ∇ G × G M ), displayed in (4.1), make equivariant gerbe connections excellent candidates for WZW terms in gauged sigma models [Wit,FOS,GSW1,GSW2,BE].…”

Section: Introductionmentioning

confidence: 99%

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A classification of equivariant gerbe connections

Park

Redden

2019

Commun. Contemp. Math.

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Let G be a compact Lie group acting on a smooth manifold M . In this paper, we consider Meinrenken's G-equivariant bundle gerbe connections on M as objects in a 2-groupoid. We prove this 2-category is equivalent to the 2-groupoid of gerbe connections on the differential quotient stack associated to M , and isomorphism classes of G-equivariant gerbe connections are classified by degree three differential equivariant cohomology. Finally, we consider the existence and uniqueness of conjugation-equivariant gerbe connections on compact semisimple Lie groups.

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“…These cohomological structures, corresponding to vector bundles twisted by the gerbe in a well-defined manner, contribute their own part to the classification scheme of consistent σ-models on world-sheets with defects and straightforwardly accommodate a variant of the orientifolding and gauging constructions set up for the bulk gerbes, as demonstrated in Refs. [GR02,Gaw05,GSW08a,GSW]. It well deserves to be pointed out that the ensuing explicit constructions of orbifold and orientifold G-branes in the controlled setting of the WZW model, presented in Refs.…”

Section: Introductionmentioning

confidence: 99%

Defects, dualities and the geometry of strings via gerbes. I. Dualities and state fusion through defects

Suszek

2011

Preprint

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This is the first of a series of papers discussing canonical aspects of the two-dimensional non-linear sigma model in the presence of conformal defects on the world-sheet in the framework of gerbe theory. In the paper, the basic tools of the state-space analysis are introduced, such as the symplectic structure on the state space of the sigma model and the pre-quantum bundle over it, and a relation between the defects and dualities of the sigma model is established. Also, a state-space description of the splitting-joining interaction of the string across the defect is presented, leading to an interpretation of the geometric data associated to junctions of defect lines in terms of intertwiners between the incoming and outgoing sectors of the theory in interaction.

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The Gauging of Two-Dimensional Bosonic Sigma Models on World-Sheets With Defects

Cited by 5 publications

References 67 publications

Global Gauge Anomalies in Coset Models of Conformal Field Theory

Global Gauge Anomalies in Coset Models of Conformal Field Theory

A classification of equivariant gerbe connections

Defects, dualities and the geometry of strings via gerbes. I. Dualities and state fusion through defects

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