Unification mechanism for gauge and spacetime symmetries

László, Á.

doi:10.1088/1751-8121/aa5c04

Cited by 4 publications

(25 citation statements)

References 18 publications

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“…Examples for case B are detailed in [12], namely the super-Poincaré group or the extended super-Poincaré group [5,15,16], as well as the extensions of the Poincaré group proposed by us [12]. Example for case C is the conformal Poincaré group, being isomorphic to SO (2,4).…”

Section: A Classification Of Poincaré Group Extensionsmentioning

confidence: 99%

“…As outlined in [12], the super-Poincaré group or extended super-Poincaré group cannot be considered as a vector bundle automorphism group with the spacetime being the base manifold. This implies that in a supersymmetric model a heavy symmetry breaking needs to be introduced in order to recover a gauge-theory-like setting, so characteristic to the Standard Model.…”

Section: Conservative Extensions Of the Poincaré Groupmentioning

confidence: 99%

“…This implies that in a supersymmetric model a heavy symmetry breaking needs to be introduced in order to recover a gauge-theory-like setting, so characteristic to the Standard Model. Also in [12] These kind of Poincaré group extensions we named conservative extensions, and are seen to have a number of rather favorable properties [12]: they are direct-indecomposable, preserve causal structure of the spacetime, preserve vector bundle structure of fundamental fields, obey positive energy condition etc. Ideally, one could look for such a setting in which case the group of compact internal symmetries is identical to the Standard Model gauge group U(1)×SU(2)×SU (3).…”

Section: Conservative Extensions Of the Poincaré Groupmentioning

confidence: 99%

“…An other example is constructed in [11,12], which is expected to be more interesting for physics. It contains a Poincaré component, a compact internal group component (U(1) in the example), and unavoidably a nilpotent internal group component.…”

Section: Conservative Extensions Of the Poincaré Groupmentioning

confidence: 99%

“…Clearly, it is essential in the construction that the radical T of the Poincaré group is extended by N , without which such a direct-indecomposability is not possible according to O'Raifeartaigh theorem. Also note, that the construction resembles to (extended) super-Poincaré group as outlined in [12], with the important difference that in case of the (extended) super-Poincaré group the translations are direct-indecomposably part of the nilpotent symmetries, called to be the group of supertranslations, forming a direct-indecomposable two-step nilpotent Lie group. In case of our construction, however, the translations are direct-decomposable from other symmetries within the radical, which makes it a conservative extension of the Poincaré group, in contrast to (extended) SUSY.…”

Section: Conservative Extensions Of the Poincaré Groupmentioning

confidence: 99%

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Possible Alternative Mechanism to SUSY: Conservative Extensions of the Poincaré Group

László

2018

Springer Proceedings in Mathematics &Amp; Statistics

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A group theoretical mechanism is outlined, which can indecomposably extend the Poincaré group by the compact internal (gauge) symmetries at the price of allowing some nilpotent (or, more precisely: solvable) internal symmetries in addition. Due to the presence of this nilpotent part, the prohibitive argument of the well known Coleman-Mandula and McGlinn no-go theorems do not go through. In contrast to SUSY or extended SUSY, in our construction the symmetries extending the Poincaré group will be all internal, i.e. they do not act on the spacetime, merely on some internal degrees of freedom -hence the name: conservative extensions of the Poincaré group. Using the Levi decomposition and O'Raifeartaigh theorem, the general structure of all possible conservative extensions of the Poincaré group is outlined, and a concrete example group is presented with U(1) being the compact gauge group component. It is argued that such nilpotent internal symmetries may be inapparent symmetries of some more fundamental field variables, and therefore do not carry an ab initio contradiction with the present experimental understanding in particle physics. The construction is compared to (extended) SUSY, since SUSY is somewhat analogous to the proposed mechanism. It is pointed out, however, that the proposed mechanism is less irregular in comparison to SUSY, in certain aspects. The only exoticity needed in comparison to a traditional gauge theory setting is that the full group of internal symmetries is not purely compact, but is a semi-direct product of a nilpotent and of a compact part.

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Section: A Classification Of Poincaré Group Extensionsmentioning

confidence: 99%

Section: Conservative Extensions Of the Poincaré Groupmentioning

confidence: 99%

Section: Conservative Extensions Of the Poincaré Groupmentioning

confidence: 99%

Section: Conservative Extensions Of the Poincaré Groupmentioning

confidence: 99%

Section: Conservative Extensions Of the Poincaré Groupmentioning

confidence: 99%

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Possible Alternative Mechanism to SUSY: Conservative Extensions of the Poincaré Group

László

2018

Springer Proceedings in Mathematics &Amp; Statistics

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Nilpotent symmetries as a mechanism for Grand Unification

Andersson

László

Ruba

2021

J. High Energ. Phys.

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In the classic Coleman-Mandula no-go theorem which prohibits the unification of internal and spacetime symmetries, the assumption of the existence of a positive definite invariant scalar product on the Lie algebra of the internal group is essential. If one instead allows the scalar product to be positive semi-definite, this opens new possibilities for unification of gauge and spacetime symmetries. It follows from theorems on the structure of Lie algebras, that in the case of unified symmetries, the degenerate directions of the positive semi-definite invariant scalar product have to correspond to local symmetries with nilpotent generators. In this paper we construct a workable minimal toy model making use of this mechanism: it admits unified local symmetries having a compact (U(1)) component, a Lorentz (SL(2, ℂ)) component, and a nilpotent component gluing these together. The construction is such that the full unified symmetry group acts locally and faithfully on the matter field sector, whereas the gauge fields which would correspond to the nilpotent generators can be transformed out from the theory, leaving gauge fields only with compact charges. It is shown that already the ordinary Dirac equation admits an extremely simple prototype example for the above gauge field elimination mechanism: it has a local symmetry with corresponding eliminable gauge field, related to the dilatation group. The outlined symmetry unification mechanism can be used to by-pass the Coleman-Mandula and related no-go theorems in a way that is fundamentally different from supersymmetry. In particular, the mechanism avoids invocation of super-coordinates or extra dimensions for the underlying spacetime manifold.

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Gravity and unification: a review

Krasnov

Percacci

2018

Class. Quantum Grav.

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We review various classical unified theories of gravity and other interactions that have appeared in the literature, paying special attention to scenarios in which spacetime remains four-dimensional, while an "internal" space is enlarged. The starting point for each such unification scenario is a particular formalism for General Relativity. We thus start by reviewing, besides the usual Einstein-Hilbert and Palatini formulations, the Einstein-Cartan, MacDowell-Mansouri and BF (both nonchiral and chiral) formulations. Each of these introduces some version of "internal" bundle and a dynamical variable that ties the internal and tangent bundles. In each of these formulations there is also an independent connection in the "internal" bundle. One can then study the effects of "enlarging the internal space", which typically leads to a theory of gravity and Yang-Mills fields.We review what has been done in the literature on each of these unification schemes, and compare and contrast their achievements to those of the better developed Kaluza-Klein scenario. * Electronic address: kirill.krasnov@nottingham.ac.uk † Electronic address: percacci@sissa.it

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Unification mechanism for gauge and spacetime symmetries

Cited by 4 publications

References 18 publications

Possible Alternative Mechanism to SUSY: Conservative Extensions of the Poincaré Group

Possible Alternative Mechanism to SUSY: Conservative Extensions of the Poincaré Group

Nilpotent symmetries as a mechanism for Grand Unification

Gravity and unification: a review

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