A Systematic Approach to Confinement in N=1 Supersymmetric Gauge Theories

We give necessary criteria for N=1 supersymmetric theories to be in a smoothly confining phase without chiral symmetry breaking and with a dynamically generated superpotential. Using our general arguments we find all such confining SU and Sp theories with a single gauge group and no tree level superpotential.Comment: 8 pages, LaTe

Pollution, Mortality and Optimal Environmental Policy

We study pollution, mortality and growth in an overlapping generations economy with uncertain lifetimes. Economic activity creates pollution: the stock of pollution has a negative effect on life expectancy while higher income (proxying either for better nutrition and immunity or for better availability of public health) has a prophylactic effect on mortality. These counteracting effects can make the growth-survival relationship non-concave and lead to multiple steady states and a poverty trap. An increase in exogenous abatement taxes can increase the basin of the poverty trap. We study a dynamically consistent sequence of secondbest abatement taxes. The optimal tax is shown to be a non-homogeneous and increasing function of the current capital stock with the optimal tax zero for low levels of capital. The feedback effect from the capital stock to the optimal tax can make optimal abatement policy an independent source of non-linearities leading to non-existence and multiplicity of steady states, as well as oscillations around some steady states when there are none under exogenous taxes

Systematic Study of Theories with Quantum Modified Moduli

We begin the process of classifying all supersymmetric theories with quantum modified moduli. We determine all theories based on a single SU or Sp gauge group with quantum modified moduli. By flowing among theories we have calculated the precise modifications to the algebraic constraints that determine the moduli at the quantum level. We find a class of theories, those with a classical constraint that is covariant but not invariant under global symmetries, that have a singular modification to the moduli, which consists of a new branch.Comment: 21 pages, ReVTeX (or Latex, etc), corrected typos and cQMM discusio

Pollution, Mortality and Time-Consistent Abatement Taxes

We study dynamically consistent policy in a neoclassical overlapping generations growth model where pollution externalities undermine health but are mitigated via tax- nanced abatement. With arbitrarily constant taxation, two steady states arise: an unstable `poverty trap' and a `neoclassical' steady state near which the dynamics might either be monotonically convergent or oscillating. When the planner chooses a time consistent abatement path that maximises a weighted intergenerational sum of expected utility, the optimal tax is zero at low levels of capital and then a weakly increasing function of the capital stock. The non-homogeneity of the tax function along with its feedback e ect on savings induces additional steady states, stability reversals and oscillations

A Comment on Zero-brane Quantum Mechanics

We consider low energy, non-relativistic scattering of two Dirichlet zero-branes as an exercise in quantum mechanics. For weak string coupling and sufficiently small velocity, the dynamics is governed by an effective U(2) gauge theory in 0+1 dimensions. At low energies, D-brane scattering can reliably probe distances much shorter than the string scale. The only length scale in the quantum mechanics problem is the eleven dimensional Planck length. This provides evidence for the role of scales shorter than the string length in the weakly coupled dynamics of type IIA strings.Comment: 9 pages, harvmac, improved treatment of 2+1 proble

Improving plan quality and consistency by standardization of dose constraints in prostate cancer patients treated with CyberKnife.

Treatment plans for prostate cancer patients undergoing stereotactic body radiation therapy (SBRT) are often challenging due to the proximity of organs at risk. Today, there are no objective criteria to determine whether an optimal treatment plan has been achieved, and physicians rely on their personal experience to evaluate the plan's quality. In this study, we propose a method for determining rectal and bladder dose constraints achievable for a given patient's anatomy. We expect that this method will improve the overall plan quality and consistency, and facilitate comparison of clinical outcomes across different institutions. The 3D proximity of the organs at risk to the target is quantified by means of the expansion-intersection volume (EIV), which is defined as the intersection volume between the target and the organ at risk expanded by 5 mm. We determine a relationship between EIV and relevant dosimetric parameters, such as the volume of bladder and rectum receiving 75% of the prescription dose (V75%). This relationship can be used to establish institution-specific criteria to guide the treatment planning and evaluation process. A database of 25 prostate patients treated with CyberKnife SBRT is used to validate this approach. There is a linear correlation between EIV and V75% of bladder and rectum, confirming that the dose delivered to rectum and bladder increases with increasing extension and proximity of these organs to the target. This information can be used during the planning stage to facilitate the plan optimization process, and to standardize plan quality and consistency. We have developed a method for determining customized dose constraints for prostate patients treated with robotic SBRT. Although the results are technology specific and based on the experience of a single institution, we expect that the application of this method by other institutions will result in improved standardization of clinical practice

Dual Descriptions of SO(10) SUSY Gauge Theories with Arbitrary Numbers of Spinors and Vectors

We examine the low energy structure of N=1 supersymmetric SO(10) gauge theory with matter chiral superfields in N_Q spinor and N_f vector representations. We construct a dual to this model based upon an SU(N_f+2N_Q-7) x Sp(2N_Q-2) gauge group without utilizing deconfinement methods. This product theory generalizes all previously known Pouliot-type duals to SO(N_c) models with spinor and vector matter. It also yields large numbers of new dual pairs along various flat directions. The dual description of the SO(10) theory satisfies multiple consistency checks including an intricate renormalization group flow analysis which links it with Seiberg's duality transformations. We discuss its implications for building grand unified theories that contain all Standard Model fields as composite degrees of freedom.Comment: 36 pages, harvmac and tables macros, 1 figur

The Interplay Between θ\theta and T

We extend a recent computation of the dependence of the free energy, F, on the noncommutative scale $\theta$ to theories with very different UV sensitivity. The temperature dependence of $F$ strongly suggests that a reduced number of degrees of freedom contributes to the free energy in the non-planar sector, $F_{\rm np}$, at high temperature. This phenomenon seems generic, independent of the UV sensitivity, and can be traced to modes whose thermal wavelengths become smaller than the noncommutativity scale. The temperature dependence of $F_{\rm np}$ can then be calculated at high temperature using classical statistical mechanics, without encountering a UV catastrophe even in large number of dimensions. This result is a telltale sign of the low number of degrees of freedom contributing to $F$ in the non-planar sector at high temperature. Such behavior is in marked contrast to what would happen in a field theory with a random set of higher derivative interactions.Comment: 14 pages, 1 eps figur