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arXiv:hep-th/9808059v1 11 Aug 1998String Fields and the Standard ModelT. DereliDepartment of Physics, Middle East Technical University,06531 Ankara, Turkeytekin@dereli.physics.metu.edu.trRobin W. TuckerDepartment of Physics, University of Lancaster,Bailrigg, Lancs. LA1 4YB, UKr.tucker@lancaster.ac.uk(9 August 1998)The Cremmer-Scherk mechanism is generalised in a non-Abelian context. In the presence of theHiggs scalars of the standard model it is argued that fields arising from the low energy effectivestring action may contribute to the mass generation of the observed vector bosons that mediatethe electroweak interactions and that future analyses of experimental data should consider thepossibility of string induced radiative corrections to the Weinberg angle coming from physics beyondthe standard model.PACS numbers: 11.15.-q, 11.15.Ex, 12.10.Kt, 12.60.CnThe standard model of fundamental particle interactions is based on families of charged leptons, quarks and scalarfields interacting via gauge fields associated with Lie groups [1],[2]. This structure is general enough to accommodategravitation and it is a common belief that an underlying geometrical theory associated with some extended structurein higher dimensions will offer a unified framework from which the standard model will emerge as an effective lowenergy approximation. Although such a unique unified geometrical theory is currently elusive, there are strong hintsthat it may manifest itself in a number of different guises. These alternative representations are said to be related bycertain duality transformations. They promise to relate different spectra associated with dual coupling regimes andoffer an explanation of the observed masses of the fundamental particles. At the level of low energy effective actions,however, current phenomenology relies on a number of alternative mechanisms for mass generation. These maybe briefly classified as (Kaluza-Klein) harmonic expansions in dimensional reduction, dynamical symmetry breakingand the Higgs mechanism based on the existence of fundamental self-coupled scalar fields. Each mechanism makesparticular predictions and experimental guidance is required for preferring one without prejudice.In this note we explore the role of the Abelian gauge vector potential A, the dilaton φ and the antisymmetric3-form gauge field H that arise in certain low energy effective actions on the Higgs mechanism of the standard model.In lowest order H is usually interpreted as describing a scalar (axion) field that, together with the dilaton scalar φ,modifies Einsteinian gravitation.1However, we propose here that H couples to vector fiel ds via an interaction withHiggs fields in such a way that it contributes to mass generation via a spontaneous breakdown of gauge symmetry.The coupling is inspired by an earlier incarnation of string theory as a dual model for the strong interactions andthe recognition that sectors associated with “Reggeons” and “Pomerons” are “dual”. The gauge potential A isanalogous to a Reggeon state in the hadron model and the Abelian gauge symmetry in the action is inherited froma representation of the Virasoro symmetry. The antisymmetric tensor field described here in terms of the 2-form B,where to lowest order H = dB, corresponds to a state in the Pomeron sector of the dual model. In 1974, Cremmer andScherk suggested on the basis of a 1-loop summation that both these fields could gain mass by radiative corrections[3],[4]. Furthermore they gave a gauge invariant effective action that maintained a duality between the Reggeon andPomeron descriptions.In the context of low energy effective string theory, the mechanism arises from the effective action density 4-formΛ[g,φ,A,B] = κR ∗ 1 −(2α − 3)4dφ ∧ ∗dφ+12e−2φdB ∧ ∗dB +12e−2φdA ∧ ∗dA + λA ∧ dB(1)where A is a 1-form, B a 2-form, φ the dilaton 0-form on spacetime M with a metric g, curvature scalar R and1The interpretation of a massless axion A is based on the field equation d(e−2φ∗ dB) = 0 so that locally dB = e2φ∗ dA andhence d(e2φ∗ dA) = 0.1