Induced Gravity II: Grand Unification

As an illustration of a renormalizable, asymptotically-free model of induced gravity, we consider an $SO(10)$ gauge theory interacting with a real scalar multiplet in the adjoint representation. We show that dimensional transmutation can occur, spontaneously breaking $SO(10)$ to $SU(5){\otimes}U(1),$ while inducing the Planck mass and a positive cosmological constant, all proportional to the same scale $v$. All mass ratios are functions of the values of coupling constants at that scale. Below this scale (at which the Big Bang may occur), the model takes the usual form of Einstein-Hilbert gravity in de Sitter space plus calculable corrections. We show that there exist regions of parameter space in which the breaking results in a local minimum of the effective action, and a {\bf positive} dilaton $(\hbox{mass})^2$ from two-loop corrections associated with the conformal anomaly. Furthermore, unlike the singlet case we considered previously, some minima lie within the basin of attraction of the ultraviolet fixed point. Moreover, the asymptotic behavior of the coupling constants also lie within the range of convergence of the Euclidean path integral, so there is hope that there will be candidates for sensible vacua. Although open questions remain concerning unitarity of all such renormalizable models of gravity, it is not obvious that, in curved backgrounds such as those considered here, unitarity is violated. In any case, any violation that may remain will be suppressed by inverse powers of the reduced Planck mass.Comment: 44 pages, 5 figures, 2 tables. v2 has new discussion concerning stability of SSB plus related appendix. Additional references added. v3 is version to be published; contains minor revision

Zero modes in de Sitter background

There are five well-known zero modes among the fluctuations of the metric of de~Sitter (dS) spacetime. For Euclidean signature, they can be associated with certain spherical harmonics on the $S^4$ sphere, viz., the vector representation $\bf5$ of the global $SO(5)$ isometry. They appear, for example, in the perturbative calculation of the on-shell effective action of dS space, as well as in models containing matter fields. These modes are shown to be associated with collective modes of $S^4$ corresponding to certain coherent fluctuations. When dS space is embedded in flat five dimensions $E^5,$ they may be seen as a legacy of translation of the center of the $S^4$ sphere. Rigid translations of the $S^4$-sphere on $E^5$ leave the classical action invariant but are unobservable displacements from the point of view of gravitational dynamics on $S^4.$ Thus, unlike similar moduli, the center of the sphere is not promoted to a dynamical degree of freedom. As a result, these zero modes do not signify the possibility of physically realizable fluctuations or flat directions for the metric of dS space. They are not associated with Killing vectors on $S^4$ but can be with certain non-isometric, conformal Killing forms that locally correspond to a rescaling of the volume element $dV_4.$ For convenience, we frame our discussion in the context of renormalizable gravity, but the conclusions apply equally to the corresponding zero modes in Einstein gravity. We expect that these zero modes will be present to all orders in perturbation theory. They will occur for Lorentzian signature as well, so long as the hyperboloid $H^4$ is locally stable, but there remain certain infrared issues that need to be clarified. We conjecture that they will appear in any gravitational theory having dS background as a locally stable solution of the effective action, regardless of whether additional matter is included.Comment: v4, 28pages, no figures; final journal form, minor changes in text and refs from v

Dred, universality and the superparticle spectrum

Recent work on the use of dimensional reduction for the regularisation of non--supersymmetric theories is reviewed. It is then shown that there exists a class of theories for which a universal form of the soft supersymmetry breaking terms is invariant under renormalisation. It is argued that this universal form might be approached as an infra--red fixed point for the unified theory above the unification scale. The superparticle spectrum is calculated for these theories.Comment: 9 pages. Uses latex and psfig. One figure in a separate postscript fil

Strictly Anomaly Mediated Supersymmetry Breaking

We consider an MSSM extension with anomaly mediation as the source of supersymmetry-breaking, and a U(1) symmetry which solves the tachyonic slepton problem, and introduces both the see-saw mechanism for neutrino masses, and the Higgs mu-term. We compare its spectra with those from so-called minimal anomaly mediated supersymmetry breaking. We find a Standard Model-like Higgs of mass 125 GeV with a gravitino mass of 140 TeV and tan(beta)=16. However, the muon anomalous magnetic moment is 3 sigma away from the experimental value. The model naturally produces a period of hybrid inflation, which can exit to a false vacuum characterised by large Higgs vevs, reaching the true ground state after a period of thermal inflation. The scalar spectral index is reduced to approximately 0.975, and the correct abundance of neutralino dark matter can be produced by decays of thermally-produced gravitinos, provided the gravitino mass (and hence the Higgs mass) is high. Naturally light cosmic strings are produced, satisfying bounds from the Cosmic Microwave Background. The complementary pulsar timing and cosmic ray bounds require that strings decay primarily via loops into gravitational waves. Unless the loops are extremely small, the next generation pulsar timing array will rule out or detect the string-derived gravitational radiation background in this model.Comment: 38 pages, 1 figure. Discussion of 125GeV Higgs possibility, and of U(1) decoupling limi

Law and Behavioral Biology

Society uses law to encourage people to behave differently than they would behave in the absence of law. This fundamental purpose makes law highly dependent on sound understandings of the multiple causes of human behavior. The better those understandings, the better law can achieve social goals with legal tools. In this Article, Professors Jones and Goldsmith argue that many long held understandings about where behavior comes from are rapidly obsolescing as a consequence of developments in the various fields constituting behavioral biology. By helping to refine law\u27s understandings of behavior\u27s causes, they argue, behavioral biology can help to improve law\u27s effectiveness and efficiency. Part I examines how and why law and behavioral biology are connected. Part II provides an introduction to key concepts in behavioral biology. Part III identifies, explores, and illustrates a wide variety of contexts in which behavioral biology can be useful to law. Part IV addresses concerns that sometimes arise when considering biological influences on human behavior

Naturalness and Dimensional Transmutation in Classically Scale-Invariant Gravity

We discuss the nature of quantum field theories involving gravity that are classically scale-invariant. We show that gravitational radiative corrections are crucial in the determination of the nature of the vacuum state in such theories, which are renormalisable, technically natural, and can be asymptotically free in all dimensionless couplings. In the pure gravity case, we discuss the role of the Gauss-Bonnet term, and we find that Dimensional Transmutation (DT) \`a la Coleman-Weinberg leads to extrema of the effective action corresponding to nonzero values of the curvature, but such that these extrema are local maxima. In even the simplest extension of the theory to include scalar fields, we show that the same phenomenon can lead to extrema that are local minima of the effective action, with both non-zero curvature and non-zero scalar vacuum expectation values, leading to spontaneous generation of the Planck mass. Although we find an asymptotically free (AF) fixed point exists, unfortunately, no running of the couplings connect the region of DT to the basin of attraction of the AF fixed point. We also find there remains a flat direction for one of the conformal modes. We suggest that in more realistic models AF and DT could be compatible, and that the same scalar vacuum expectation values could be responsible both for DT and for spontaneous breaking of a Grand Unified gauge group.Comment: 49 pages, 4 figures, JHEP3; v2 includes additional references, one equation replaced, note added, but no substantive changes. v3 corrects beta-functions (below eq. E.1) & Table 2, fixed typos and format, acknowledgements. v4 contains additional references and slight revisions in text. v5 is the published JHEP version, with no changes in results or conclusion