Leibniz-Yang-Mills gauge theories and the 2-Higgs mechanism

Strobl, Thomas

doi:10.1103/physrevd.99.115026

Cited by 11 publications

(15 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We finally display the relevant part of the action functional for this sector of the theory. For this purpose it is convenient to define the following generalization of the curvatures or field strengths relevant for the n = 2 Leibniz theory [20,22] (but cf. also [25,36]):…”

Section: The Gauge Field Sector Of Gauged Maximal Supergravity In D =mentioning

confidence: 99%

“…as shown in detail in [22]. The relevant part of the action functional then is, at least schematically, of the following form, cf., e.g., [34][35][36]:…”

Section: )mentioning

confidence: 99%

“…Leibniz gauge theories can be considered also independently as particular higher gauge theories in their own right, cf., e.g., [22,25,36,37]. In that case, a functional of the form (3.53), to which one may add also M κ 4 (G, * G) , (3.56) depends only on the fields A and B.…”

Section: )mentioning

confidence: 99%

See 2 more Smart Citations

The Embedding Tensor, Leibniz–Loday Algebras, and Their Higher Gauge Theories

Kotov

Strobl

2019

Commun. Math. Phys.

Self Cite

View full text Add to dashboard Cite

We show that the data needed for the method of the embedding tensor employed in gauging supergravity theories are precisely those of a Leibniz algebra (with one of its induced quotient Lie algebras embedded into a rigid symmetry Lie algebra that provides an additional "representation constraint"). Every Leibniz algebra gives rise to a Lie n-algebra in a canonical way (for every n ∈ N ∪ {∞}). It is the gauging of this L ∞ -algebra that explains the tensor hierarchy of the bosonic sector of gauged supergravity theories. The tower of p-from gauge fields corresponds to Lyndon words of the universal enveloping algebra of the free Lie algebra of an odd vector space in this construction. Truncation to some n yields the reduced field content needed in a concrete spacetime dimension.

show abstract

Section: The Gauge Field Sector Of Gauged Maximal Supergravity In D =mentioning

confidence: 99%

“…as shown in detail in [22]. The relevant part of the action functional then is, at least schematically, of the following form, cf., e.g., [34][35][36]:…”

Section: )mentioning

confidence: 99%

See 1 more Smart Citation

The Embedding Tensor, Leibniz–Loday Algebras, and Their Higher Gauge Theories

Kotov

Strobl

2019

Commun. Math. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Leibniz algebras, embedding tensors and their associated tensor hierarchies provide a nice and efficient way to construct supergravity theories and further to higher gauge theories (see e.g. [6,7,18,24,51] and references therein for a rich physics literature on this subject, and see [27,28] for a math-friendly introduction on this subject). Recently, this topic has attracted much attention of the mathematical physics world.…”

Section: Introductionmentioning

confidence: 99%

The Controlling $$L_\infty $$-Algebra, Cohomology and Homotopy of Embedding Tensors and Lie–Leibniz Triples

Sheng

Tang

Zhu

2021

Commun. Math. Phys.

View full text Add to dashboard Cite

In this paper, we first construct the controlling algebras of embedding tensors and Lie–Leibniz triples, which turn out to be a graded Lie algebra and an $$L_\infty $$ L ∞ -algebra respectively. Then we introduce representations and cohomologies of embedding tensors and Lie–Leibniz triples, and show that there is a long exact sequence connecting various cohomologies. As applications, we classify infinitesimal deformations and central extensions using the second cohomology groups. Finally, we introduce the notion of a homotopy embedding tensor which will induce a Leibniz$$_\infty $$ ∞ -algebra. We realize Kotov and Strobl’s construction of an $$L_\infty $$ L ∞ -algebra from an embedding tensor, as a functor from the category of homotopy embedding tensors to that of Leibniz$$_\infty $$ ∞ -algebras, and a functor further to that of $$L_\infty $$ L ∞ -algebras.

show abstract

“…In order to motivate our definition of extension, let us begin by noticing that in the current literature we find many ways to extend Yang-Mills theories, such as those in [27,25,8,49,50,51,52,19,22,53,42,15,20]. We note that most of them can be organized into three classes: deformations, addition of a correction term and extension of the gauge group.…”

Section: Introductionmentioning

confidence: 99%

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

Martins,

Campos,

Biezuner

2020

Preprint

View full text Add to dashboard Cite

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 [34] 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.

show abstract

Leibniz-Yang-Mills gauge theories and the 2-Higgs mechanism

Cited by 11 publications

References 31 publications

The Embedding Tensor, Leibniz–Loday Algebras, and Their Higher Gauge Theories

The Embedding Tensor, Leibniz–Loday Algebras, and Their Higher Gauge Theories

The Controlling $$L_\infty $$-Algebra, Cohomology and Homotopy of Embedding Tensors and Lie–Leibniz Triples

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

Contact Info

Product

Resources

About