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General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
Abstract:
In conventional gauge theories, any local gauge symmetry generator is
accompanied by a corresponding gauge boson in order to compensate the
transformation of the gauge-covariant derivation against the local gauge
transformations as acting on the matter fields. Indeed, whenever the gauge
group is purely compact, as in usual gauge theories, the invocation of
corresponding gauge bosons as compensating fields is unavoidable. That is
because there exist no nontrivial forgetful homomorphisms onto some smaller Lie
groups from the full gauge group. In this paper we show a mechanism that at the
price of allowing some non-semisimple component of the gauge group besides the
compact part, it is possible to construct such Lagrangians that the
non-semisimple part of the local gauge group only acts on the matter fields,
without invoking corresponding gauge bosons. It shall be shown that already the
ordinary Dirac equation admits such a hidden symmetry related to the dilatation
group, thus this mechanism cannot be called unphysical. Then, we give our more
complicated example Lagrangian, in which the gauge group is an indecomposable
Lie group built up of a nilpotent part and of a compact part. Since the
nilpotent part does carry also Lorentz charges in our example, the first order
symmetries of the pertinent theory give rise to a unified gauge--Poincar\'e
group, bypassing Coleman--Mandula and related no-go theorems in a different way
in comparison to SUSY. The existence of a local symmetry without a gauge boson
is already mathematically very striking, but this new mechanism might even be
useful to eventually try to substitute SUSY for a unification concept of
symmetries.
