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Pré-Publication, Document De Travail Année : 2020

On Extensions of Yang-Mills-Type Theories, Their Spaces and Their Categories

Résumé

In this paper we consider the classification problem of extensions of Yang-Mills-type (YMT) theories. For us, a YMT theory differs from the classical Yang-Mills theories by allowing an arbitrary pairing on the curvature. The space of YMT theories with a prescribed gauge group G and instanton sector P is classified, an upper bound to its rank is given and it is compared with the space of Yang-Mills theories. We present extensions of YMT theories as a simple and unified approach to many different notions of deformations and addition of correction terms previously discussed in the literature. A relation between these extensions and emergence phenomena in the sense of arXiv:2004.13144 is presented. We consider the space of all extensions of a fixed YMT theory S G and we prove that for every additive group action of G in R and every commutative and unital ring R, this space has an induced structure of R[G]-module bundle. We conjecture that this bundle can be continuously embedded into a trivial bundle. Morphisms between extensions of a fixed YMT theory are defined in such a way that they define a category of extensions. It is proved that this category is a reflective subcategory of a slice category, reflecting some properties of its limits and colimits.
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Dates et versions

hal-02907894 , version 1 (27-07-2020)

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  • HAL Id : hal-02907894 , version 1

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Yuri Ximenes Martins, Luiz Felipe Andrade Campos, Rodney Josué Biezuner. On Extensions of Yang-Mills-Type Theories, Their Spaces and Their Categories. 2020. ⟨hal-02907894⟩

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