The ABJM model is a higher gauge theory

Palmer, Sam; Saemann, Christian

doi:10.1142/s0219887814500753

Cited by 19 publications

(24 citation statements)

References 21 publications

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“…Altogether, we see that the Heisenberg Lie p-algebra of S n is a central extension of the Lie algebra so(n + 1) to a Lie p-algebra. This result matches an important expectation: In the case n = 3, the resulting Lie 2algebra agrees at the level of vector spaces with the 3-Lie algebra A 4 underlying the BLG model [7,8]; see also [55] and [75] for connections of this model with higher gauge theory.…”

Section: Quantization and Emergence Of Multisymplectic Manifoldssupporting

confidence: 83%

L∞-algebra models and higher Chern–Simons theories

Ritter

Sämann

2016

Rev. Math. Phys.

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We continue our study of zero-dimensional field theories in which the fields take values in a strong homotopy Lie algebra. In a first part, we review in detail how higher Chern-Simons theories arise in the AKSZ-formalism. These theories form a universal starting point for the construction of L ∞ -algebra models. We then show how to describe superconformal field theories and how to perform dimensional reductions in this context. In a second part, we demonstrate that Nambu-Poisson and multisymplectic manifolds are closely related via their Heisenberg algebras. As a byproduct of our discussion, we find central Lie palgebra extensions of so(p + 2). Finally, we study a number of L ∞ -algebra models which are physically interesting and which exhibit quantized multisymplectic manifolds as vacuum solutions.arXiv:1511.08201v3 [hep-th]

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Section: Quantization and Emergence Of Multisymplectic Manifoldssupporting

confidence: 83%

L∞-algebra models and higher Chern–Simons theories

Ritter

Sämann

2016

Rev. Math. Phys.

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“…First, it is certainly worthwhile to explore the relation to the ABJM model in detail. Since the latter model is a higher gauge theory [29] and contains a Chern-Simons term, there is now hope that a link to boundary ABJM theory analogous to e.g. [30] is possible.…”

Section: Discussionmentioning

confidence: 99%

The non-abelian self-dual string

2019

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We argue that the relevant higher gauge group for the non-abelian generalization of the self-dual string equation is the string 2-group. We then derive the corresponding equations of motion and discuss their properties. The underlying geometric picture is a string structure, i.e. a categorified principal bundle with connection whose structure 2-group is the string 2-group. We readily write down the explicit elementary solution to our equations, which is the categorified analogue of the 't Hooft-Polyakov monopole. Our solution passes all the relevant consistency checks; in particular, it is globally defined on R 4 and approaches the abelian self-dual string of charge one at infinity. We note that our equations also arise as the BPS equations in a recently proposed six-dimensional superconformal field theory and we show that with our choice of higher gauge structure, the action of this theory can be naturally reduced to four-dimensional supersymmetric Yang-Mills theory.

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“…Furthermore, one can in principle regard M2-brane models as higher gauge theories. [20] This is again encouraging, since we expect some relation between the (2,0)-theory and the M2-brane models.…”

Section: ∞ -Algebrasmentioning

confidence: 53%

“…The last example is interesting in our context as the 3‐Lie algebras relevant in M2‐brane models are, in fact, of this type [], see also []. Furthermore, one can in principle regard M2‐brane models as higher gauge theories . This is again encouraging, since we expect some relation between the (2,0)‐theory and the M2‐brane models.…”

Section: Higher Gauge Theoriesmentioning

confidence: 60%

Higher Structures, Self‐Dual Strings and 6d Superconformal Field Theories

Sämann

2019

Fortschritte der Physik

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I summarize and discuss some recent results on formulating actions of six‐dimensional superconformal field theories using the language of higher gauge theory. The latter guarantees mathematical consistency of our constructions and we review crucial aspects of this framework, such as L∞‐algebras and corresponding kinematical data given by higher connections. We then show that there is a mathematically consistent non‐Abelian extension of the self‐dual string equation which satisfies many physical expectations. Our construction favors a particular higher gauge group leading us to higher principal bundles known as string structures. Using these, we manage to formulate a six‐dimensional action which shares many properties with the famous (2,0)‐theory but also still differs from it in some key points.

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The ABJM model is a higher gauge theory

Cited by 19 publications

References 21 publications

L∞-algebra models and higher Chern–Simons theories

L∞-algebra models and higher Chern–Simons theories

The non-abelian self-dual string

Higher Structures, Self‐Dual Strings and 6d Superconformal Field Theories

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