Causal Fermion Systems: An Elementary Introduction to Physical Ideas and Mathematical Concepts

We give an elementary introduction to the theory of causal fermion systems, with a focus on the underlying physical ideas and the conceptual and mathematical foundations.Comment: 24 pages, LaTeX, 3 figures, minor changes (published version

Top and Bottom Seesaw from Supersymmetric Strong Dynamics

We propose a top and bottom seesaw model with partial composite top and bottom quarks. Such composite quarks and topcolor gauge bosons are bound states from supersymmetric strong dynamics by Seiberg duality. Supersymmetry breaking also induces the breaking of topcolor into the QCD gauge coupling. The low energy description of our model reduces to a complete non-minimal extension of the top seesaw model with bottom seesaw. The non-minimal nature is crucial for Higgs mixings and the appearance of light Higgs fields. The Higgs fields are bound states of partial composite particles with the lightest one compatible with a 125 GeV Higgs field which was discovered at the LHC.Comment: Minor changes, Published Versio

Partially Composite Higgs in Supersymmetry

We propose a framework for natural breaking of electroweak symmetry in supersymmetric models, where elementary Higgs fields are semi-perturbatively coupled to a strong superconformal sector. The Higgs VEVs break conformal symmetry in the strong sector at the TeV scale, and the strong sector in turn gives important contributions to the Higgs potential, giving rise to a kind of Higgs bootstrap. A Higgs with mass 125\GeV can be accommodated without any fine tuning. A Higgsino mass of order the Higgs mass is also dynamically generated in these models. The masses in the strong sector generically violate custodial symmetry, and a good precision electroweak fit requires tuning of order $\sim 10$. The strong sector has an approximately supersymmetric spectrum of hadrons at the TeV scale that can be observed by looking for a peak in the $WZ$ invariant mass distribution, as well as final states containing multiple $W$, $Z$, and Higgs bosons. The models also generically predict large corrections (either enhancement or suppression) to the h \to \ga\ga width.Comment: 31 page

Two-Point Functions and S-Parameter in QCD-like Theories

We calculated the vector, axial-vector, scalar and pseudo-scalar two-point functions up to two-loop level in the low-energy effective field theory for three different QCD-like theories. In addition we also calculated the pseudo-scalar decay constant $G_M$. The QCD-like theories we used are those with fermions in a complex, real or pseudo-real representation with in general n flavours. These case correspond to global symmetry breaking pattern of $SU(n)_L\times SU(n)_R\to SU(n)_V$, $SU(2n)\to SO(2n)$ or $SU(2n)\to Sp(2n)$. We also estimated the S parameter for those different theories.Comment: 29 page

The quantum mechanics of perfect fluids

We consider the canonical quantization of an ordinary fluid. The resulting long-distance effective field theory is derivatively coupled, and therefore strongly coupled in the UV. The system however exhibits a number of peculiarities, associated with the vortex degrees of freedom. On the one hand, these have formally a vanishing strong-coupling energy scale, thus suggesting that the effective theory's regime of validity is vanishingly narrow. On the other hand, we prove an analog of Coleman's theorem, whereby the semiclassical vacuum has no quantum counterpart, thus suggesting that the vortex premature strong-coupling phenomenon stems from a bad identification of the ground state and of the perturbative degrees of freedom. Finally, vortices break the usual connection between short distances and high energies, thus potentially impairing the unitarity of the effective theory.Comment: 35 page

Lorentz-Violating Supergravity

The standard forms of supersymmetry and supergravity are inextricably wedded to Lorentz invariance. Here a Lorentz-violating form of supergravity is proposed. The superpartners have exotic properties that are not possible in a theory with exact Lorentz symmetry and microcausality. For example, the bosonic sfermions have spin 1/2 and the fermionic gauginos have spin 1. The theory is based on a phenomenological action that is shown to follow from a simple microscopic and statistical picture.Comment: 15 pages; to be published in Proceedings of Beyond the Desert 2003 (Castle Ringberg, Tegernsee, Germany, 9-14 June 2003), edited by H. V. Klapdor-Kleingrothau

Application of the operator product expansion to the short distance behavior of nuclear potentials

We investigate the short distance behavior of nucleon-nucleon (NN) potentials defined through Bethe-Salpeter wave functions, by perturbatively calculating anomalous dimensions of 6-quark operators in QCD. Thanks to the asymptotic freedom of QCD, 1-loop computations give certain exact results for the potentials in the zero distance limit. In particular the functional form of the S-state central NN potential at short distance $r$ is predicted to be a little weaker than $r^{-2}$. On the other hand, due to the intriguing character of the anomalous dimension spectrum, perturbative considerations alone can not determine whether this potential is repulsive or attractive at short distances. A crude estimation suggests that the force at short distance is repulsive, as found numerically in lattice QCD. A similar behavior is found for the tensor potential.Comment: 40 pages, no figure

Spontaneous Parity Violation in SUSY Strong Gauge Theory

We suggest simple models of spontaneous parity violation in supersymmetric strong gauge theory. We focus on left-right symmetric model and investigate vacuum with spontaneous parity violation. Non-perturbative effects are calculable in supersymmetric gauge theory, and we suggest two new models. The first model shows confinement, and the second model has a dual description of the theory. The left-right symmetry breaking and electroweak symmetry breaking are simultaneously occurred with the suitable energy scale hierarchy. The second model also induces spontaneous supersymmetry breaking.Comment: 14 page

Progress in One-Loop QCD Computations

We review progress in calculating one-loop scattering amplitudes required for next-to-leading-order corrections to QCD processes. The underlying technical developments include the spinor helicity formalism, color decompositions, supersymmetry, string theory, factorization and unitarity. We provide explicit examples illustrating these techniques.Comment: To appear in Annual Reviews of Nuclear and Particle Science (1996

One Loop Renormalization of the Littlest Higgs Model

In Little Higgs models a collective symmetry prevents the Higgs from acquiring a quadratically divergent mass at one loop. This collective symmetry is broken by weakly gauged interactions. Terms, like Yukawa couplings, that display collective symmetry in the bare Lagrangian are generically renormalized into a sum of terms that do not respect the collective symmetry except possibly at one renormalization point where the couplings are related so that the symmetry is restored. We study here the one loop renormalization of a prototypical example, the Littlest Higgs Model. Some features of the renormalization of this model are novel, unfamiliar form similar chiral Lagrangian studies.Comment: 23 pages, 17 eps figure