NEW PARTICLES AND INTERACTIONS

We analyze the manifestations of new matter particles predicted by models of new physics beyond the Standard Model, at present and future high--energy colliders. We consider both the production of these new particles and some of their indirect signatures at $pp$ and $eP$ colliders as well as TeV \ee colliders with their \ee, e \gamma, \gamma \gamma and $e^- e^-$ modes. The report is arranged into four main sections plus an overview. These sections will deal separately with exotic and excited fermions, difermions, and new interactions.Comment: 64 pages, latex, 30 figures (not included). The full *.ps file including the figures can be obtained via anonymous ftp at ftp://lpsvsh.lps.umontreal.ca/hep_th/dpf.ps . To appear as a chapter in "Electroweak Symmetry Breaking and Beyond the Standard Model", edited by T. Barklow, S. Dawson, H.E. Haber and S. Siegrist, World Scientifi

Quenched Computation of the Complexity of the Sherrington-Kirkpatrick Model

The quenched computation of the complexity in the Sherrington-Kirkpatrick model is presented. A modified Full Replica Symmetry Breaking Ansatz is introduced in order to study the complexity dependence on the free energy. Such an Ansatz corresponds to require Becchi-Rouet-Stora-Tyutin supersymmetry. The complexity computed this way is the Legendre transform of the free energy averaged over the quenched disorder. The stability analysis shows that this complexity is inconsistent at any free energy level but the equilibirum one. The further problem of building a physically well defined solution not invariant under supersymmetry and predicting an extensive number of metastable states is also discussed.Comment: 19 pages, 13 figures. Some formulas added corrected, changes in discussion and conclusion, one figure adde

Complexity in Mean-Field Spin-Glass Models: Ising pp-spin

The Complexity of the Thouless-Anderson-Palmer (TAP) solutions of the Ising $p$-spin is investigated in the temperature regime where the equilibrium phase is one step Replica Symmetry Breaking. Two solutions of the resulting saddle point equations are found. One is supersymmetric (SUSY) and includes the equilibrium value of the free energy while the other is non-SUSY. The two solutions cross exactly at a value of the free energy where the replicon eigenvalue is zero; at low free energy the complexity is described by the SUSY solution while at high free energy it is described by the non-SUSY solution. In particular the non-SUSY solution describes the total number of solutions, like in the Sherrington-Kirkpatrick (SK) model. The relevant TAP solutions corresponding to the non-SUSY solution share the same feature of the corresponding solutions in the SK model, in particular their Hessian has a vanishing isolated eigenvalue. The TAP solutions corresponding to the SUSY solution, instead, are well separated minima.Comment: 13 pages, 9 figure