Differential Characters

Bär, Christian; Becker, Christian

doi:10.1007/978-3-319-07034-6

Cited by 31 publications

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“…Finally, from the definitions of C A2 and p G,A1 , the last formula of the statement follows. 4 The homology map on the moduli space of flat connections 4.1 Chern-Simons characters on M × A/G Given a principal G-bundle π : P → M , let G ⊂ GauP be a subgroup of GauP such that G acts freely on the space of connections A and A → A/G is a principal G-bundle. For example we can take G the subgroup of gauge transformations fixing a point p 0 ∈ P (see e.g.…”

Section: Equivariant Characteristic Classesmentioning

confidence: 99%

Differential characters and cohomology of the moduli of flat connections

López

Pérez

2018

Lett Math Phys

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Let π : P → M be a principal bundle and p an invariant polynomial of degree r on the Lie algebra of the structure group. The theory of Chern-Simons differential characters is exploited to define an homology mapthe moduli space of flat connections of π under the action of a subgroup G of the gauge group. The differential characters of first order are related to the Dijkgraaf-Witten action for Chern-Simons Theory. The second order characters are interpreted geometrically as the holonomy of a connection in a line bundle over F/G). The relationship with other constructions in the literature is also analyzed.Mathematics Subject Classification 2010: 53C05, 55R40, 51H25.

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Section: Equivariant Characteristic Classesmentioning

confidence: 99%

Differential characters and cohomology of the moduli of flat connections

López

Pérez

2018

Lett Math Phys

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“…We recall the definition of differential characters (see [11] and [5] for details). We denote by C k (N ) and Z k (N ) the smooth chains and cycles on N .…”

Section: Cheeger-simons Differential Charactersmentioning

confidence: 99%

“…We recall (e.g. see [5]) that χ(u) is invariant under reparametrizations, i.e. if u : U → N , and ϕ is an orientation preserving diffeomorphism of U , then χ(u•ϕ) = χ(u).…”

Section: Cheeger-simons Differential Charactersmentioning

confidence: 99%

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Equivariant prequantization bundles on the space of connections and characteristic classes

Pérez¹

2018

Annali di Matematica

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We show how characteristic classes determine equivariant prequantization bundles over the space of connections on a principal bundle. These bundles are shown to generalize the Chern-Simons line bundles to arbitrary dimensions. Our result applies to arbitrary bundles, and it is studied the action of both the gauge group and the automorphisms group. The action of the elements in the connected component of the identity of the group generalizes known results in the literature. The action of the elements not connected with the identity is shown to be determined by a characteristic class by using differential characters and equivariant cohomology. We extend our results to the space of Riemannian metrics and the actions of diffeomorphisms. In dimension 2, a ΓM -equivariant prequantization bundle of the Weil-Petersson symplectic form on the Teichmüller space is obtained, where ΓM is the mapping class group of the surface M .Mathematics Subject Classification 2100: Primary 53C05; Secondary 53C08, 70S15, 58D27.

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“…While there exist many different models in addition, like Deligne cohomology[74], the de Rham-Federer model[75] or Hopkins-Singer differential cocycles[76], they were all shown[57,58] to be isomorphic to H • (. ).…”

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confidence: 99%

Aspects of higher-abelian gauge theories at zero and finite temperature: Topological Casimir effect, duality and Polyakov loops

Kelnhofer

2019

Nuclear Physics B

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Higher-abelian gauge theories associated with Cheeger-Simons differential characters are studied on compact manifolds without boundary. The paper consists of two parts: First the functional integral formulation based on zeta function regularization is revisited and extended in order to provide a general framework for further applications. A field theoretical model -called extended higher-abelian Maxwell theory -is introduced, which is a higher-abelian version of Maxwell theory of electromagnetism extended by a particular topological action. This action is parametrized by two non-dynamical harmonic forms and generalizes the θ-term in usual gauge theories. In the second part the general framework is applied to study the topological Casimir effect in higher-abelian gauge theories at finite temperature at equilibrium. The extended higher-abelian Maxwell theory is discussed in detail and an exact expression for the free energy is derived. A non-trivial topology of the background space-time modifies the spectrum of both the zero-point fluctuations and the occupied states forming the thermal ensemble. The vacuum (Casimir) energy has two contributions: one related to the propagating modes and the second one related to the topologically inequivalent configurations of higher-abelian gauge fields. In the high temperature limit the leading term is of Stefan-Boltzmann type and the topological contributions are suppressed. With a particular choice of parameters extended higher-abelian Maxwell theories of different degrees are shown to be dual. On the n-dimensional torus we provide explicit expressions for the thermodynamic functions in the low-and high temperature regimes, respectively. Finally, the impact of the background topology on the two-point correlation function of a higher-abelian variant of the Polyakov loop operator is analyzed.1 The reviews [2, 3, 4, 5, 6, 7] and the references therein cover also further aspects of the topological Casimir effect. Due to the vast amount of literature we are well aware that our selection may by no means be complete.

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Differential Characters

Cited by 31 publications

References 0 publications

Differential characters and cohomology of the moduli of flat connections

Differential characters and cohomology of the moduli of flat connections

Equivariant prequantization bundles on the space of connections and characteristic classes

Aspects of higher-abelian gauge theories at zero and finite temperature: Topological Casimir effect, duality and Polyakov loops

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