Dividing the Indivisible: Procedures for Allocating Cabinet Ministries to Political Parties in a Parliamentary System

Political parties in Northern Ireland recently used a divisor method of apportionment to choose, in sequence, ten cabinet ministries. If the parties have complete information about each others' preferences, we show that it may not be rational for them to act sincerely by choosing their most-preferred ministry that is available. One consequence of acting sophisticatedly is that the resulting allocation may not be Pareto-optimal, making all the parties worse off. Another is nonmonotonicty-choosing earlier may hurt rather than help a party. We introduce a mechanism that combines sequential choices with a structured form of trading that results in sincere choices for two parties. Although there are difficulties in extending this mechanism to more than two parties, other approaches are explored, such as permitting parties to making consecutive choices not prescribed by an apportionment method. But certain problems, such as eliminating envy, remain.APPORTIONMENT METHODS; CABINETS; SEQUENTIAL ALLOCATION; MECHANISM DESIGN; FAIRNESS

Fermions on an Interval: Quark and Lepton Masses without a Higgs

We consider fermions on an extra dimensional interval. We find the boundary conditions at the ends of the interval that are consistent with the variational principle, and explain which ones arise in various physical circumstances. We apply these results to higgsless models of electroweak symmetry breaking, where electroweak symmetry is not broken by a scalar vacuum expectation value, but rather by the boundary conditions of the gauge fields. We show that it is possible to find a set of boundary conditions for bulk fermions that would give a realistic fermion mass spectrum without the presence of a Higgs scalar, and present some sample fermion mass spectra for the standard model quarks and leptons as well as their resonances.Comment: LaTeX, 36 pages, 5 figure

RS1, Custodial Isospin and Precision Tests

We study precision electroweak constraints within a RS1 model with gauge fields and fermions in the bulk. The electroweak gauge symmetry is enhanced to SU(2)_L \times SU(2)_R \times U(1)_{B-L}, thereby providing a custodial isospin symmetry sufficient to suppress excessive contributions to the T parameter. We then construct complete models, complying with all electroweak constraints, for solving the hierarchy problem, without supersymmetry or large hierarchies in the fundamental couplings. Using the AdS/CFT correspondence our models can be interpreted as dual to a strongly coupled conformal Higgs sector with global custodial symmetry, gauge and fermionic matter being fundamental fields external to the CFT. This scenario has interesting collider signals, distinct from other RS models in the literature.Comment: 32 pages, 6 figures, latex2e, minor changes, references adde

Cosmological Consequences of Nearly Conformal Dynamics at the TeV scale

Nearly conformal dynamics at the TeV scale as motivated by the hierarchy problem can be characterized by a stage of significant supercooling at the electroweak epoch. This has important cosmological consequences. In particular, a common assumption about the history of the universe is that the reheating temperature is high, at least high enough to assume that TeV-mass particles were once in thermal equilibrium. However, as we discuss in this paper, this assumption is not well justified in some models of strong dynamics at the TeV scale. We then need to reexamine how to achieve baryogenesis in these theories as well as reconsider how the dark matter abundance is inherited. We argue that baryonic and dark matter abundances can be explained naturally in these setups where reheating takes place by bubble collisions at the end of the strongly first-order phase transition characterizing conformal symmetry breaking, even if the reheating temperature is below the electroweak scale $\sim 100$ GeV. We also discuss inflation as well as gravity wave smoking gun signatures of this class of models.Comment: 22 pages, 7 figure

K* nucleon hyperon form factors and nucleon strangeness

A crucial input for recent meson hyperon cloud model estimates of the nucleon matrix element of the strangeness current are the nucleon-hyperon-K* (NYK*) form factors which regularize some of the arising loops. Prompted by new and forthcoming information on these form factors from hyperon-nucleon potential models, we analyze the dependence of the loop model results for the strange-quark observables on the NYK* form factors and couplings. We find, in particular, that the now generally favored soft N-Lambda-K* form factors can reduce the magnitude of the K* contributions in such models by more than an order of magnitude, compared to previous results with hard form factors. We also discuss some general implications of our results for hadronic loop models.Comment: 9 pages, 8 figures, new co-author, discussion extended to the momentum dependence of the strange vector form factor

The phase transition in QCD with broken SU(2) flavour symmetry

We report the first investigation of the QCD transition temperature, T_c, for two flavours of staggered quarks with unequal masses at lattice spacings of 1/4T. On changing the u/d quark mass ratio in such a way that m(pi_0)^2/m(pi_+)^2 changes from 1 to 0.78, thus bracketing the physical value of this ratio, we find that T_c remains unchanged in units of both m_rho and Lambda_MSbar.Comment: 12 pages, 5 figure

Effective Field Theory for Dilute Fermions with Pairing

Effective field theory (EFT) methods for a uniform system of fermions with short-range, natural interactions are extended to include pairing correlations, as part of a program to develop a systematic Kohn-Sham density functional theory (DFT) for medium and heavy nuclei. An effective action formalism for local composite operators leads to a free-energy functional that includes pairing by applying an inversion method order by order in the EFT expansion. A consistent renormalization scheme is demonstrated for the uniform system through next-to-leading order, which includes induced-interaction corrections to pairing.Comment: 31 pages, 10 figures, affiliation updated, paper unchange

Energy Loss versus Shadowing in the Drell-Yan Reaction on Nuclei

We present a new analysis of the E772 and E866 experiments on the nuclear dependence of Drell-Yan (DY) lepton pair production resulting from the bombardment of $^2H$, Be, C, Ca, Fe, and W targets by 800 GeV/c protons at Fermilab. We employ a light-cone formulation of the DY reaction in the rest frame of the nucleus, where the dimuons detected at small values of Bjorken x_2 << 1 may be considered to originate from the decay of a heavy photon radiated from an incident quark in a bremsstrahlung process. We infer the energy loss of the quark by examining the suppression of the nuclear-dependent DY ratios seen as a function of projectile momentum fraction x_1 and dimuon mass M. Shadowing, which also leads to nuclear suppression of dimuons, is calculated within the same approach employing the results of phenomenological fits to deep inelastic scattering data from HERA. The analysis yields -dE/dz =2.73 +/- 0.37 +/- 0.5 GeV/fm for the rate of quark energy loss per unit path length, a value consistent with theoretical expectations including the effects of the inelastic interaction of the incident proton at the surface of the nucleus. This is the first observation of a nonzero energy loss effect in such experiments.Comment: 43 pages including 17 figure

Improved results for N=(2,2) super Yang-Mills theory using supersymmetric discrete light-cone quantization

We consider the (1+1)-dimensional ${\cal N}=(2,2)$ super Yang--Mills theory which is obtained by dimensionally reducing ${\cal N}=1$ super Yang--Mills theory in four dimension to two dimensions. We do our calculations in the large-$N_c$ approximation using Supersymmetric Discrete Light Cone Quantization. The objective is to calculate quantities that might be investigated by researchers using other numerical methods. We present a precision study of the low-mass spectrum and the stress-energy correlator $$. We find that the mass gap of this theory closes as the numerical resolution goes to infinity and that the correlator in the intermediate $r$ region behaves like $r^{-4.75}$.Comment: 18 pages, 8 figure

A classification of smooth embeddings of 3-manifolds in 6-space

We work in the smooth category. If there are knotted embeddings S^n\to R^m, which often happens for 2m<3n+4, then no concrete complete description of embeddings of n-manifolds into R^m up to isotopy was known, except for disjoint unions of spheres. Let N be a closed connected orientable 3-manifold. Our main result is the following description of the set Emb^6(N) of embeddings N\to R^6 up to isotopy. The Whitney invariant W : Emb^6(N) \to H_1(N;Z) is surjective. For each u \in H_1(N;Z) the Kreck invariant \eta_u : W^{-1}u \to Z_{d(u)} is bijective, where d(u) is the divisibility of the projection of u to the free part of H_1(N;Z). The group Emb^6(S^3) is isomorphic to Z (Haefliger). This group acts on Emb^6(N) by embedded connected sum. It was proved that the orbit space of this action maps under W bijectively to H_1(N;Z) (by Vrabec and Haefliger's smoothing theory). The new part of our classification result is determination of the orbits of the action. E. g. for N=RP^3 the action is free, while for N=S^1\times S^2 we construct explicitly an embedding f : N \to R^6 such that for each knot l:S^3\to R^6 the embedding f#l is isotopic to f. Our proof uses new approaches involving the Kreck modified surgery theory or the Boechat-Haefliger formula for smoothing obstruction.Comment: 32 pages, a link to http://www.springerlink.com added, to appear in Math. Zei