Standard model with gravity couplings

Abstract

PACS number(s): 04.62.+v, 11.30.Er In this paper, we examine the coupling of matter fields to gravity within the framework of the Standard Model of particle physics. The coupling is described in terms of Weyl fermions of a definite chirality, and employs only (anti)self-dual or left-handed spin connection fields. It is known from the work of Ashtekar and others that such fields can furnish a complete description of gravity without matter. We show that conditions ensuring the cancellation of perturbative chiral gauge anomalies are not disturbed. We also explore a global anomaly associated with the theory, and argue that its removal requires that the number of fundamental fermions in the theory must be multiples of 16. In addition, we investigate the behavior of the theory under discrete transformations P, C and T; and discuss possible violations of these discrete symmetries, including CPT, in the presence of instantons and the Adler-Bell-Jackiw anomaly.

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“…For example, if the VEV isθ = M1, i.e. flat space, the term m µν nµν η mn (4) generates a mass term of the form M 2 (A mnp − A pnm )(A mnp − A pnm ). A similar phenomenon occurs with the Palatini action.…”

“…The symmetric components of H cannot be eliminated in this way: after suitably dealing with the diffeomorphism invariance, they correspond to the graviton field. It is possible to show that they are also the Goldstone bosons for a larger GL (4) internal symmetry [2]; this is useful if one wants to discuss more general theories where the connection is allowed not to be metric, but this will not be needed for the purposes of this paper. The main conclusion of this discussion is that gravity is a gauge theory in the Higgs (broken) phase, and that a 'symmetric' phase would correspond to vanishingθ and hence vanishing metric 4 .…”

“…In the present work, we begin to discuss this unification mechanism from the bottom up, starting from the weak interactions, rather than postulating from the outset what the unified 4 Because in the vierbein formulation we are used to maintaining explicit invariance under the local Lorentz transformations, the statement that the local Lorentz invariance is broken spontaneously may cause some confusion. The fact is that gauge symmetries are never broken: in the Higgs phenomenon it is the choice of the unitary gauge that breaks the gauge invariance, but we are free to chose any other gauge if we want to.…”

“…Although we shall not use it explicitly, the reformulation of general relativity in terms of Ashtekar variables, which emphasizes the role of the selfdual part of the connection, is close in spirit to this work. We refer to [4] for a previous look at the standard model from this point of view. In addition to [1], the symmetry breaking aspects of gravity have also been studied in [7,8].…”

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“…In this respect, spin network states are holomorphic in A and are therefore also not automatically P-invariant. Further discussions on possible P, CP and CPT violations in Ashtekar theory coupled to matter have been discussed elsewhere [7].…”