We investigate worlds that lie on a slice through the parameter space of the standard model over which quark masses vary. We allow as many as three quarks to participate in nuclei, while fixing the mass of the electron and the average mass of the lightest baryon flavor multiplet. We classify as congenial worlds that satisfy the environmental constraint that the quark masses allow for stable nuclei with charge one, six, and eight, making organic chemistry possible. Whether a congenial world actually produces observers capable of measuring those quark masses depends on a multitude of historical contingencies, beginning with primordial nucleosynthesis and including other astrophysical processes, which we do not explore. Such constraints may be independently superimposed on our results. Environmental constraints such as the ones we study may be combined with information about the a priori distribution of quark masses over the landscape of possible universes to determine whether the measured values of the quark masses are determined environmentally, but our analysis is independent of such an anthropic approach. We estimate baryon masses as functions of quark masses via first-order perturbation theory in flavor $SU(3)$ breaking. We estimate nuclear masses as functions of the baryon masses using two separate tools: for a nucleus made of two baryon species, when possible we consider its analog in our world, a nucleus with a similar binding energy, up to Coulomb contributions. For heavy nuclei or nuclei made of more than two baryons, we develop a generalized Weizsäcker semiempirical mass formula, in which strong kinematic flavor symmetry violation is modeled by a degenerate Fermi gas . We check for the stability of nuclei against fission, strong particle emission (analogous to $\alpha$ decay), and weak nucleon emission. For two light quarks with charges $2/3$ and $-1/3$ , we find a band of congeniality roughly 29 MeV wide in their mass difference, with our own world lying comfortably away from the edges. We also find another, less robust region of congeniality with one light, charge $-1/3$ quark, and two heavier, approximately degenerate quarks with charges $-1/3$ and $2/3$. No other assignment of light quark charges yields congenial worlds with two baryons participating in nuclei. We identify the region in quark mass space where nuclei would be made from three or more baryon species. We discuss issues relevant to the congeniality of such worlds, but a full characterization of them is left for future investigation.

We present a series of supersymmetric models exhibiting an entirely new vacuum structure: towers of metastable vacua with higher and higher energies. As the number of vacua grows towards infinity, the energy of the highest vacuum remains fixed while the energy of the true ground state tends towards zero. We study the instanton-induced tunneling dynamics associated with such vacuum towers and find that many distinct decay patterns along the tower are possible: these include not only regions of vacua experiencing direct collapses and/or tumbling cascades, but also other regions of vacua whose stability is protected by “great walls” as well as regions of vacua populating “forbidden cities” into which tunneling cannot occur. We also discuss possible applications of this setup for the cosmological-constant problem, for studies of the string landscape, for supersymmetry breaking, and for $Z^{\prime }$ phenomenology. Finally, we point out that a limiting case of our setup yields theories with yet another new vacuum structure: infinite numbers of degenerate vacua. As a result, the true ground states of such theories are Bloch waves, with energy eigenvalues approximating a continuum and giving rise to a vacuum “band” structure.

We propose a comprehensive theory of dark matter that explains the recent proliferation of unexpected observations in high-energy astrophysics. Cosmic ray spectra from ATIC and PAMELA require a WIMP (weakly interacting massive particle). with mass $M_{\chi }\sim 500–800\mathrm{GeV}$ that annihilates into leptons at a level well above that expected from a thermal relic. Signals from WMAP and EGRET reinforce this interpretation. Limits on $\overline{p}$ and ${\pi }^0\mathrm{\text{−}}\gamma$’s constrain the hadronic channels allowed for dark matter. Taken together, we argue these facts imply the presence of a new force in the dark sector, with a Compton wavelength $m_{\varphi }^{-1}\gtrsim 1{\mathrm{GeV}}^{-1}$. The long range allows a Sommerfeld enhancement to boost the annihilation cross section as required, without altering the weak-scale annihilation cross section during dark matter freeze-out in the early universe. If the dark matter annihilates into the new force carrier $\varphi$, its low mass can make hadronic modes kinematically inaccessible, forcing decays dominantly into leptons. If the force carrier is a non-Abelian gauge boson, the dark matter is part of a multiplet of states, and splittings between these states are naturally generated with size $\alpha m_{\varphi }\sim \mathrm{MeV}$, leading to the eXciting dark matter (XDM) scenario previously proposed to explain the positron annihilation in the galactic center observed by the INTEGRAL satellite; the light boson invoked by XDM to mediate a large inelastic scattering cross section is identified with the $\varphi$ here. Somewhat smaller splittings would also be expected, providing a natural source for the parameters of the inelastic dark matter (iDM) explanation for the DAMA annual modulation signal. Since the Sommerfeld enhancement is most significant at low velocities, early dark matter halos at redshift $\sim 10$ potentially produce observable effects on the ionization history of the universe. Because of the enhanced cross section, detection of substructure is more probable than with a conventional WIMP. Moreover, the low velocity dispersion of dwarf galaxies and Milky Way subhalos can increase the substructure annihilation signal by an additional order of magnitude or more.

We derive the general form for a three-dimensional scale-invariant field theory with $\mathcal{N}=6$ supersymmetry, $SU(4)$ R-symmetry and a $U(1)$ global symmetry. The results can be written in terms of a 3-algebra in which the triple product is not antisymmetric. For a specific choice of 3-algebra we obtain the $\mathcal{N}=6$ theories that have been recently proposed as models for M2-branes in an ${\mathbb{R}}^8/{\mathbb{Z}}_k$ orbifold background.

We analyze macroscopic effects of TeV-scale black holes, such as could possibly be produced at the LHC, in what is regarded as an extremely hypothetical scenario in which they are stable and, if trapped inside Earth, begin to accrete matter. We examine a wide variety of TeV-scale gravity scenarios, basing the resulting accretion models on first-principles, basic, and well-tested physical laws. These scenarios fall into two classes, depending on whether accretion could have any macroscopic effect on the Earth at times shorter than the Sun’s natural lifetime. We argue that cases with such an effect at shorter times than the solar lifetime are ruled out, since in these scenarios black holes produced by cosmic rays impinging on much denser white dwarfs and neutron stars would then catalyze their decay on time scales incompatible with their known lifetimes. We also comment on relevant lifetimes for astronomical objects that capture primordial black holes. In short, this study finds no basis for concerns that TeV-scale black holes from the LHC could pose a risk to Earth on time scales shorter than the Earth’s natural lifetime. Indeed, conservative arguments based on detailed calculations and the best-available scientific knowledge, including solid astronomical data, conclude, from multiple perspectives, that there is no risk of any significance whatsoever from such black holes.

We discuss a realization of the nonrelativistic conformal group (the Schrödinger group) as the symmetry of a spacetime. We write down a toy model in which this geometry is a solution to field equations. We discuss various issues related to nonrelativistic holography. In particular, we argue that free fermions and fermions at unitarity correspond to the same bulk theory with different choices for the near-boundary asymptotics corresponding to the source and the expectation value of one operator. We describe an extended version of nonrelativistic general coordinate invariance which is realized holographically.

We discuss possible ways to observationally detect the superdense cosmic objects composed of hypothetical subconstituent fermions beneath the quark/lepton level, recently proposed by us. The characteristic mass and size of such objects depend on the compositeness scale, and their huge density cannot arise within a context of quarks and leptons alone. Their eventual observation would therefore be a direct vindication of physics beyond the standard model of particle physics, possibly far beyond the reach of the Large Hadron Collider (LHC), in a relatively simple and inexpensive manner. If relic objects of this type exist, they can possibly be detected by present and future x-ray observatories, high-frequency gravitational wave detectors, and seismological detectors. To have a realistic detection rate, i.e., to be observable, they must necessarily constitute a significant fraction of cold dark matter.

We investigate and solve in the context of general relativity the apparent paradox which appears when bodies floating in a background fluid are set in relativistic motion. Suppose some macroscopic body, say, a submarine designed to lie just in equilibrium when it rests (totally) immersed in a certain background fluid. The puzzle arises when different observers are asked to describe what is expected to happen when the submarine is given some high velocity parallel to the direction of the fluid surface. On the one hand, according to observers at rest with the fluid, the submarine would contract and, thus, sink as a consequence of the density increase. On the other hand, mariners at rest with the submarine using an analogous reasoning for the fluid elements would reach the opposite conclusion. The general relativistic extension of the Archimedes law for moving bodies shows that the submarine sinks. As an extra bonus, this problem suggests a new gedankenexperiment for the generalized second law of thermodynamics.

Merging compact binaries are currently regarded as the most promising source of gravitational waves for the planned Earth-based LIGO/VIRGO laser-interferometer detector system, and will be an important source also for similar, lower-frequency detectors that might be flown in space (e.g., the proposed LISA mission). During the orbital inspiral, if one or both bodies are rapidly rotating, the general relativistic spin-orbit and spin-spin coupling (i.e., the "dragging of inertial frames" by the bodies' spins) cause the binary's orbital plane to precess. In this paper we analyze the resulting modulation of the inspiral gravitational waveform, using ${\mathrm{post}}^2$-Newtonian equations to describe the precession of the orbital plane, but only the leading-order (Newtonian, quadrupole-moment approximation) equations to describe the orbit, the radiation reaction, the inspiral, and the wave generation. We derive all the formulas one needs to readily compute the spin-modulated gravitational waveform (within the post-Newtonian approximation and the approximation that the precession frequency is much smaller than the orbital frequency). We also develop intuition into what the modulated signals "look like," by a variety of means. We provide approximate, analytical solutions for the precessional motion and the modulated waveforms for two important special cases: the case where the bodies have nearly equal masses and the case where one of the bodies has negligible spin. For these cases, for almost all choices of binary parameters, the motion is a simple precession of the orbital angular momentum around the nearly fixed direction of the total angular momentum, with a few tens of precession periods as the waves sweep through the LIGO/VIRGO observational band. However, when the spin and orbital angular momenta are approximately anti-aligned, there is a transitional-precession epoch during which their near cancellation causes the binary to "lose its gyroscopic bearings" and tumble in space, with a corresponding peculiar sweep of the waveform modulation. We also explore numerically the precessional behaviors that occur for general masses and spins; these typically appear quite similar to our special-case, simple-precession, and transitional-precession solutions. An Appendix develops several diagrammatic aids for understanding intuitively the relation between the precessing orbit and the modulated waveform.

Unified electroweak gauge theories based on the gauge group $\mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_L\times \mathrm{SU}{\mathrm{}\left(2\right)\mathrm{}}_R\times \mathrm{U}{\mathrm{}\left(1\right)\mathrm{}}_{B-L}$, in which the breakdown of parity invariance is spontaneous, lead most naturally to a massive neutrino. Assuming the neutrino to be a Majorana particle, we show that smallness of its mass can be understood as a result of the observed maximality of parity violation in low-energy weak interactions. This result is shown to be independent of the number of generations and unaffected by renormalization effects. Phenomenological consequences of this model at low energies are studied. Observation of neutrinoless double-$\beta$ decay will provide a crucial test of this class of models. Implications for rare decays such as $\mu \to e\gamma$, $\mu \to \mathrm{ee}\overline{e}$, etc. are also noted. It is pointed out that in the realm of neutral-current phenomena, departure from the predictions of the standard model for polarized-electron-hadron scattering, forward-backward asymmetry in $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$, and neutrino interactions has a universal character and may be therefore used as a test of the model.

Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization-group techniques and their application to scaling phenomena. The renormalization-group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large spacelike momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3) × SU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken and that the severe infrared singularities prevent the occurrence of noncolor singlet physical states. The deep-inelastic structure functions, as well as the electron-positron total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive light-cone or parton-model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.