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UV-complete 4-derivative scalar field theory
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A scalar field theory with 4-derivative kinetic terms and 4-derivative cubic and quartic couplings is presented as a proxy for quantum quadratic gravity (QQG). The scalar theory is renormalizable and asymptotically free and the remaining key issue is unitarity, or more precisely positivity, just as it is in QQG. We have extended calculations for the optical theorem and for a differential cross section, both in the high energy limit, to show how positivity constrains the theory. The results also show how it is that differential cross sections can have good high energy behavior. Finally we use the scalar theory to extend the Stuckelberg theory of a massive U(1) gauge boson to a renormalizable theory of a self-interacting gauge boson.
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Fixed points of classical gravity coupled with a Standard-Model-like theory
A free conformal matter content with n1/2=4n1 and n'_0=3n1 gives a UV fixed point where all stress tensor correlators are finite; the Standard Model with right-handed neutrinos and 36 four-derivative scalars is such a theory.
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