Symmetry Breaking Constraints: Recent Results

Symmetry is an important problem in many combinatorial problems. One way of dealing with symmetry is to add constraints that eliminate symmetric solutions. We survey recent results in this area, focusing especially on two common and useful cases: symmetry breaking constraints for row and column symmetry, and symmetry breaking constraints for eliminating value symmetryComment: To appear in Proceedings of Twenty-Sixth Conference on Artificial Intelligence (AAAI-12

Dark Matter, Baryon Asymmetry, and Spontaneous B and L Breaking

We investigate the dark matter and the cosmological baryon asymmetry in a simple theory where baryon (B) and lepton (L) number are local gauge symmetries that are spontaneously broken. In this model, the cold dark matter candidate is the lightest new field with baryon number and its stability is an automatic consequence of the gauge symmetry. Dark matter annihilation is either through a leptophobic gauge boson whose mass must be below a TeV or through the Higgs boson. Since the mass of the leptophobic gauge boson has to be below the TeV scale one finds that in the first scenario there is a lower bound on the elastic cross section of about 5x10^{-46} cm^2. Even though baryon number is gauged and not spontaneously broken until the weak scale, a cosmologically acceptable baryon excess is possible. There is tension between achieving both the measured baryon excess and the dark matter density.Comment: 23 pages, 5 figures; revised version, typos removed, references added, discussion expande

Abstraction-based action ordering in planning

Many planning problems contain collections of symmetric objects, actions and structures which render them difficult to solve efficiently. It has been shown that the detection and exploitation of symmetric structure in planning problems can dramatically reduce the size of the search space and the time taken to find a solution. We present the idea of using an abstraction of the problem domain to reveal symmetric structure and guide the navigation of the search space. We show that this is effective even in domains in which there is little accessible symmetric structure available for pruning. Proactive exploitation represents a flexible and powerfulalternative to the symmetry-breaking strategies exploited in earlier work in planning and CSPs. The notion of almost symmetry is defined and results are presented showing that proactive exploitation of almost symmetry can improve the performance of a heuristic forward search planner

Dark Matter and Dark Forces from a supersymmetric hidden sector

We show that supersymmetric "Dark Force" models with gravity mediation are viable. To this end, we analyse a simple string-inspired supersymmetric hidden sector model that interacts with the visible sector via kinetic mixing of a light Abelian gauge boson with the hypercharge. We include all induced interactions with the visible sector such as neutralino mass mixing and the Higgs portal term. We perform a detailed parameter space scan comparing the produced dark matter relic abundance and direct detection cross sections to current experiments.Comment: 40 pages, 11 figures comprising 21 plots. 4Mb total size. v2: figures and references updated; typos removed; some extra explanations added. Matches version published in PR

Implications of SUSY Model Building

We discuss the motivations and implications of models of low-energy supersymmetry. We present the case for the minimal supersymmetric standard model, which we define to include the minimal particle content and soft supersymmetry-breaking interactions which are universal at the GUT or Planck scale. This model is in agreement with all present experimental results, and yet depends on only a few unknown parameters and therefore maintains considerable predictive power. From the theoretical side, it arises naturally in the context of supergravity models. We discuss radiative electroweak symmetry breaking and the superpartner spectrum in this scenario, with some added emphasis on regions of parameter space leading to unusual or interesting experimental signals at future colliders. We then examine how these results may be affected by various modifications and extensions of the minimal model, including GUT effects, extended gauge, Higgs, and matter sectors, non-universal supersymmetry breaking, non-conservation of R-parity, and dynamical supersymmetry breaking at low energies.Comment: Contribution to the DPF long range study, working group on 'Electroweak Symmetry Breaking and Beyond the SM Physics'; LaTeX file without figures, 60 pages. The complete PS file, including figures, can be obtained by anonymous ftp from ftp://phenom.physics.wisc.edu/pub/preprints/1995/madph-95-879.ps.

Axion Protection from Flavor

The QCD axion fails to solve the strong CP problem unless all explicit PQ violating, Planck-suppressed, dimension n<10 operators are forbidden or have exponentially small coefficients. We show that all theories with a QCD axion contain an irreducible source of explicit PQ violation which is proportional to the determinant of the Yukawa interaction matrix of colored fermions. Generically, this contribution is of low operator dimension and will drastically destabilize the axion potential, so its suppression is a necessary condition for solving the strong CP problem. We propose a mechanism whereby the PQ symmetry is kept exact up to n=12 with the help of the very same flavor symmetries which generate the hierarchical quark masses and mixings of the SM. This "axion flavor protection" is straightforwardly realized in theories which employ radiative fermion mass generation and grand unification. A universal feature of this construction is that the heavy quark Yukawa couplings are generated at the PQ breaking scale.Comment: 16 pages, 2 figure