Optimality Conditions and Duality for Semi-Infinite Mathematical Programming Problem with Equilibrium Constraints

This article considers a semi-infinite mathematical programming problem with equilibrium constraints (SIMPEC) defined as a semi-infinite mathematical programming problem with complementarity constraints. We establish necessary and sufficient optimality conditions for the (SIMPEC). We also formulate Wolfe- and Mond-Weir-type dual models for (SIMPEC) and establish weak, strong and strict converse duality theorems for (SIMPEC) and the corresponding dual problems under invexity assumptions.

Top polarization as a probe of new physics

We investigate the effects of new physics scenarios containing a high mass vector resonance on top pair production at the LHC, using the polarization of the produced top. In particular we use kinematic distributions of the secondary lepton coming from top decay, which depends on top polarization, as it has been shown that the angular distribution of the decay lepton is insensitive to the anomalous tbW vertex and hence is a pure probe of new physics in top quark production. Spin sensitive variables involving the decay lepton are used to reconstruct the top polarization. Some sensitivity is found for the new couplings of the top.

Path-integral derivation of the superconformal anomaly for the N=1 supersymmetric Yang-Mills theory

Fujikawa's method of evaluating the supercurrent and the superconformal current anomalies, using the heat-kernel regularization scheme, is extended to theories with gauge invariance, in particular, to the off-shell N=1 supersymmetric Yang-Mills (SSYM) theory. The Jacobians of supersymmetry and superconformal transformations are finite. Although the gauge-fixing term is not supersymmetric and the regularization scheme is not manifestly supersymmetric, we find that the regularized Jacobians are gauge invariant and finite and they can be expressed in such a way that there is no one-loop supercurrent anomaly for the N=1 SSYM theory. The superconformal anomaly is nonzero and the anomaly agrees with a similar result obtained using other methods.

Dynamical generation of flavour

We propose the generation of Standard Model fermion hierarchy by the extension of renormalizable SO(10) GUT with O(N (g) ) family gauge symmetry. In this scenario, Higgs representations of SO(10) also carry family indices and are called Yukawons. Vacuum expectation values of these Yukawon fields break GUT and family symmetry and generate MSSM Yukawa couplings dynamically. We have demonstrated this idea using Higgs irrep, ignoring the contribution of 1 2 0-plet which is, however, required for complete fitting of fermion mass-mixing data. The effective MSSM matter fermion couplings to the light Higgs pair are determined by the null eigenvectors of the MSSM-type Higgs doublet superfield mass matrix . A consistency condition on the doublet (1,2,+/- 1]) mass matrix ( 0) is required to keep one pair of Higgs doublets light in the effective MSSM. We show that the Yukawa structure generated by null eigenvectors of are of generic kind required by the MSSM. A hidden sector with a pair of (S (a b) ; I center dot (a b) ) fields breaks supersymmetry and facilitates 0. SUSY breaking is communicated via supergravity. In this scenario, matter fermion Yukawa couplings are reduced from 15 to just 3 parameters in MSGUT with three generations.

Duality and energy averaging for e+e- annihilation in potential models

Analytical expressions for the corrections to duality are obtained for nonsingular potentials, and are found to be small numerically. An alternative consistent way of energy smoothing, developed by Strutinsky, is elucidated. This may be of use even when potential models are not valid.

On the determination of energy eigenvalues and coupling strengths using duality

The Shifman-Vainshtein-Zakharov method of determining the eigenvalues and coupling strengths, from the operator product expansion, for the current correlation functions is studied in the nonrelativistic context, using the semiclassical expansion. The relationship between the low-lying eigenvalues, and the leading corrections to the imaginary-time Green function is elucidated by comparing systems which have almost identical spectra. In the case of an anharmonic oscillator it is found that with the procedure stated in the paper, that inclusion of more terms to the asymptotic expansion does not show any simple trend towards convergence to the exact values. Generalization to higher partial waves is given. In particular for the P-level of the oscillator, the procedure gives poorer results than for the S-level, although the ratio of the two comes out much better.

On the duality between rate and power optimizations

Sequence design problems are considered in this paper. The problem of sum power minimization in a spread spectrum system can be reduced to the problem of sum capacity maximization, and vice versa. A solution to one of the problems yields a solution to the other. Subsequently, conceptually simple sequence design algorithms known to hold for the white-noise case are extended to the colored noise case. The algorithms yield an upper bound of 2N - L on the number of sequences where N is the processing gain and L the number of non-interfering subsets of users. If some users (at most N - 1) are allowed to signal along a limited number of multiple dimensions, then N orthogonal sequences suffice.

Proposal for generalised supersymmetry Les Houches Accord for see-saw models and PDG numbering scheme

The SUSY Les Houches Accord (SLHA) 2 extended the first SLHA to include various generalisations of the Minimal Supersymmetric Standard Model (MSSM) as well as its simplest next-to-minimal version. Here, we propose further extensions to it, to include the most general and well-established see-saw descriptions (types I/II/III, inverse, and linear) in both an effective and a simple gauged extension of the MSSM framework. In addition, we generalise the PDG numbering scheme to reflect the properties of the particles. (c) 2012 Elsevier B.V. All rights reserved.

Renormalization group invariants and sum rules in the deflected mirage mediation supersymmetry breaking

We examine the deflected mirage mediation supersymmetry breaking (DMMSB) scenario, which combines three supersymmetry breaking scenarios, namely anomaly mediation, gravity mediation and gauge mediation using the one-loop renormalization group invariants (RGIs). We examine the effects on the RGIs at the threshold where the gauge messengers emerge, and derive the supersymmetry breaking parameters in terms of the RGIs. We further discuss whether the supersymmetry breaking mediation mechanism can be determined using a limited set of invariants, and derive sum rules valid for DMMSB below the gauge messenger scale. In addition we examine the implications of the measured Higgs mass for the DMMSB spectrum.

Supersymmetry: Boundary conditions and edge states

When spatial boundaries are inserted, supersymmetry (SUSY) can be broken. We have shown that in an N = 2 supersymmetric theory, all local boundary conditions allowed by self-adjointness of the Hamiltonian break N = 2 SUSY, while only a few of these boundary conditions preserve N = 1 SUSY. We have also shown that for a subset of the boundary conditions compatible with N = 1 SUSY, there exist fermionic ground states which are localized near the boundary. We also show that only very few nonlocal boundary conditions like periodic boundary conditions preserve full N = 2 supersymmetry, but none of them exhibits edge states.

Positive isotropic curvature and self-duality in dimension 4

We study a positivity condition for the curvature of oriented Riemannian 4-manifolds: the half-PIC condition. It is a slight weakening of the positive isotropic curvature (PIC) condition introduced by M. Micallef and J. Moore. We observe that the half-PIC condition is preserved by the Ricci flow and satisfies a maximality property among all Ricci flow invariant positivity conditions on the curvature of oriented 4-manifolds. We also study some geometric and topological aspects of half-PIC manifolds.

Use of transverse polarization to probe R-parity violating supersymmetry at ILC

In supersymmetric theories with R-parity violation, squarks and sleptons can mediate Standard Model fermion–fermion scattering processes. These scalar exchanges in e+e− initiated reactions can give new signals at future linear colliders. We explore use of transverse beam polarization in the study of these signals in the process View the MathML source. We highlight certain asymmetries, which can be constructed due to the existence of the transverse beam polarization, which offer discrimination from the Standard Model (SM) background and provide increased sensitivity to the R-parity violating couplings.

Boson-fermion duality in SU(m vertical bar n) supersymmetric Haldane-Shastry spin chain

By using the Y(gl(m|n)) super Yangian symmetry of the SU(m|n) supersymmetric Haldane-Shastry spin chain, we show that the partition function of this model satisfies a duality relation under the exchange of bosonic and fermionic spin degrees of freedom. As a byproduct of this study of the duality relation, we find a novel combinatorial formula for the super Schur polynomials associated with some irreducible representations of the Y(gl(m|n)) Yangian algebra. Finally, we reveal an intimate connection between the global SU(m|n) symmetry of a spin chain and the boson-fermion duality relation. (C) 2007 Elsevier B.V. All rights reserved.

Four generations: SUSY and SUSY breaking

We revisit four generations within the context of supersymmetry. Wecompute the perturbativity limits for the fourth generation Yukawa couplings and show that if the masses of the fourth generation lie within reasonable limits of their present experimental lower bounds, it is possible to have perturbativity only up to scales around 1000 TeV. Such low scales are ideally suited to incorporate gauge mediated supersymmetry breaking, where the mediation scale can be as low as 10-20 TeV. The minimal messenger model, however, is highly constrained. While lack of electroweak symmetry breaking rules out a large part of the parameter space, a small region exists, where the fourth generation stau is tachyonic. General gauge mediation with its broader set of boundary conditions is better suited to accommodate the fourth generation.

On duality in linear fractional programming

In this paper, a dual of a given linear fractional program is defined and the weak, direct and converse duality theorems are proved. Both the primal and the dual are linear fractional programs. This duality theory leads to necessary and sufficient conditions for the optimality of a given feasible solution. A unmerical example is presented to illustrate the theory in this connection. The equivalence of Charnes and Cooper dual and Dinkelbach’s parametric dual of a linear fractional program is also established.