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.

Applications of Gauge/Gravity Duality to QCD and Heavy Ion Collisions

The description of quarks and gluons, using the theory of quantum chromodynamics (QCD), has been known for a long time. Nevertheless, many fundamental questions in QCD remain unanswered. This is mainly due to problems in solving the theory at low energies, where the theory is strongly interacting. AdS/CFT is a duality between a specific string theory and a conformal field theory. Duality provides new tools to solve the conformal field theory in the strong coupling regime. There is also some evidence that using the duality, one can get at least qualitative understanding of how QCD behaves at strong coupling. In this thesis, we try to address some issues related to QCD and heavy ion collisions, applying the duality in various ways.

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.

Twisted duality symmetry and integrability of hybrid superstring on AdS(2) x S-2

IEECAS SKLLQG

Gauge/gravity duality and the interplay of various fractional branes

We consider different types of fractional branes on a Z2 orbifold of the conifold and analyze in detail the corresponding gauge/gravity duality. The gauge theory possesses a rich and varied dynamics, both in the UV and in the IR. We find the dual supergravity solution, which contains both untwisted and twisted 3-form fluxes, related to what are known as deformation and N=2 fractional branes, respectively. We analyze the resulting renormalization group flow from the supergravity perspective, by developing an algorithm to easily extract it. We find hints of a generalization of the familiar cascade of Seiberg dualities due to a nontrivial interplay between the different types of fractional branes. We finally consider the IR behavior in several limits, where the dominant effective dynamics is either confining in a Coulomb phase or runaway, and discuss the resolution of singularities in the dual geometric background. © 2008 The American Physical Society.

Positive almost Dunford-Pettis operators and their duality

We study some properties of almost Dunford-Pettis operators and we characterize pairs of Banach lattices for which the adjoint of an almost Dunford-Pettis operator inherits the same property and look at conditions under which an operator is almost Dunford-Pettis whenever its adjoint is.