Division algebras and supersymmetry III

Huerta, John

doi:10.4310/atmp.2012.v16.n5.a4

Cited by 10 publications

(15 citation statements)

References 55 publications

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“…We focus especially on the case of smooth tricategories, as this part is new. Our previous paper [27] includes the full definition of smooth categories and smooth bicategories, so here we only recall the main ideas.…”

Section: Smooth Categories and Bicategoriesmentioning

confidence: 99%

“…At a deeper level, we find this connection leads to 'higher gauge theory', a kind of gauge theory suitable for describing the parallel transport not merely of particles but of extended objects, such as strings and membranes. This is the fourth in a series of papers exploring the relationship between supersymmetry and division algebras [6,7,27], the first two of which were coauthored with John Baez. In the first paper [6], we reviewed the known story of how the division algebras give rise to the supersymmetry of super-Yang-Mills theory.…”

Section: Introductionmentioning

confidence: 98%

“…In the second [7], we made contact with higher gauge theory: we showed how the division algebras can be used to construct 'Lie 2-superalgebras' superstring(n + 1, 1), which extend the Poincaré superalgebra in the superstring dimensions n + 2 = 3, 4, 6 and 10, and 'Lie 3-superalgebras' 2-brane(n + 2, 1) in the super-2-brane dimensions n + 3 = 4, 5, 7 and 11. In our previous paper [27], we described a geometric method to integrate these Lie 2-superalgebras to '2-supergroups'. Here we employ the same method to integrate the Lie 3-superalgebras to '3supergroups'.…”

Section: Introductionmentioning

confidence: 99%

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Division algebras and supersymmetry IV

Huerta

2017

Advances in Theoretical and Mathematical Physics

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Recent work applying higher gauge theory to the superstring has indicated the presence of 'higher symmetry', and the same methods work for the super-2-brane. In the previous paper in this series, we used a geometric technique to construct a 'Lie 2-supergroup' extending the Poincaré supergroup in precisely those spacetime dimensions where the classical Green-Schwarz superstring makes sense: 3, 4, 6 and 10. In this paper, we use the same technique to construct a 'Lie 3-supergroup' extending the Poincaré supergroup in precisely those spacetime dimensions where the classical Green-Schwarz super-2-brane makes sense: 4, 5, 7 and 11. Because the geometric tools are identical, our focus here is on the precise definition of a Lie 3-supergroup.

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Section: Smooth Categories and Bicategoriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Division algebras and supersymmetry IV

Huerta

2017

Advances in Theoretical and Mathematical Physics

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“…In fact, non-Abelian YM theories are supersymmetric (thus giving rise to SYM's) only if the space-time dimension is D = 3, 4, 6 or 10 (and the same is true for the Green-Schwarz superstring), named critical dimension. In this context, the consistent formulation of Susy relies on the vanishing of a certain trilinear expression relying on the existence of A, whose real dimension is respectively given by D − 2 [27,23,28,29,30].…”

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confidence: 99%

“…In fact, there is a deep relationship between supersymmetry and division algebras; cfr. e.g [23,28,29,30],. and Refs.…”

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Klein and conformal superspaces, split algebras and spinor orbits

2017

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We discuss N = 1 Klein and Klein-Conformal superspaces in D = (2, 2) space-time dimensions, realizing them in terms of their functor of points over the split composition algebra C s . We exploit the observation that certain split forms of orthogonal groups can be realized in terms of matrix groups over split composition algebras; this leads to a natural interpretation of the the sections of the spinor bundle in the critical split dimensions D = 4, 6 and 10 as C 2 s , H 2 s and O 2 s , respectively. Within this approach, we also analyze the non-trivial spinor orbit stratification that is relevant in our construction since it affects the Klein-Conformal superspace structure. IntroductionSupersymmetry (Susy) is a deep and elegant symmetry relating half-integer spin fields (fermions, constituents of matter) to integer-spin fields (bosons, giving rise to interactions). Such a symmetry was originally formulated, as a global symmetry of fields, back in the early 70's in former Soviet Union by physicists Gol'fand and Likhtman [1], Volkov and Akulov [2], and independently in Europe by Wess and Zumino [3].A major advance in the formulation of supersymmetric theories in space-time, which then allowed for the construction of manifestly invariant interactions, was due to Salam and Strathdee, who were the first to introduce the concept of superfield [4,5]. In fact, depending on the number s and t of spacelike resp. timelike dimensions, space-time Susy recasts bosonic and fermionic fields into multiplet structures, each providing a certain representation of such an underlying symmetry. Within the simplest formulation of Susy, in which a unique fermionic generator exists besides the bosonic ones, fields defined in a space M s,t ∼ = R s,t (which in the case s = 3 and t = 1 yields the usual Minkowski space-time) are assembled into a unique object, named superfield, defined into the so-called N = 1, (s + t)-dimensional superspace M s,t|1 , which is characterized by the presence of an anti-commuting Grassmannian coordinate besides the usual commuting bosonic coordinates of M s,t .Such developments eventually led to major advances in Quantum Field Theory, constituting the foundational pillars on which consistent candidates for a unified theory encompassing Quantum Gravity and the Standard Model of particle interactions were constructed. In combination with local gauge invariance, global Susy allowed for the formulation of Supersymmetric Yang-Mills Theories (SYM's) [6]. In such a framework, Susy gives rise to remarkable cancellations between bosons and fermions in their quantum corrections, thus allowing for a study of SYM's beyond perturbation theory. This generally provides a framework for a possible solution of the hierarchy problem, for the search of natural candidates for dark matter, as well as for addressing the conceptual issue of the dark energy.In presence of general diffeomorphisms covariance, Susy becomes a local symmetry. In 1976, Ferrara, Freedman, Van Niewenhuizen [7] and Deser and Zumino [8] succeeded in formulating Su...

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Global symmetries of Yang-Mills squared in various dimensions

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Borsten

Hughes

et al. 2016

J. High Energ. Phys.

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Tensoring two on-shell super Yang-Mills multiplets in dimensions D ≤ 10 yields an on-shell supergravity multiplet, possibly with additional matter multiplets. Associating a (direct sum of) division algebra(s) D with each dimension 3 ≤ D ≤ 10 we obtain a formula for the supergravity U-duality G and its maximal compact subgroup H in terms of the internal global symmetry algebras of each super Yang-Mills theory. We extend our analysis to include supergravities coupled to an arbitrary number of matter multiplets by allowing for non-supersymmetric multiplets in the tensor product.

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Division algebras and supersymmetry III

Cited by 10 publications

References 55 publications

Division algebras and supersymmetry IV

Division algebras and supersymmetry IV

Klein and conformal superspaces, split algebras and spinor orbits

Global symmetries of Yang-Mills squared in various dimensions

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