N=1 Dualities for Exceptional Gauge Groups and Quantum Global Symmetries

We discuss our attempts to generalize the known examples of dualities in N=1 supersymmetric gauge theories to exceptional gauge groups. We derive some dual pairs from known examples connected to exceptional groups and find an interesting phenomenon: sometimes the full global symmetry is ``hidden'' on the magnetic side. It is not realized as a symmetry on the fundamental fields in the Lagrangian. Rather, it emerges as a symmetry of the quantum theory. We then focus on an approach based on self-dual models. We construct duals for some very special matter content of $E_ 7$, $E_6$ and $F_4$. Again we find that the full global symmetry is not realized on the fundamental fields.Comment: 17 pages, LaTeX2e, using utarticle.cls (included

Molien Function for Duality

The Molien function counts the number of independent group invariants of a representation. For chiral superfields, it is invariant under duality by construction. We illustrate how it calculates the spectrum of supersymmetric gauge theories.Comment: 6 pages, clarifications to sections 3,4 and a reference added, thanks to O. Aharony, C. Cummins and A. Schwimme

Exact Results in SO(11) SUSY Gauge Theories with Spinor and Vector Matter

We investigate the confining phase vacuum structure of supersymmetric SO(11) gauge theories with one spinor matter field and Nf \le 6 vectors. We describe several useful tricks and tools that facilitate the analysis of these chiral models and many other theories of similar type. The forms of the Nf=5 and Nf=6 quantum moduli spaces are deduced by requiring that they reproduce known results for SU(5) SUSY QCD along the spinor flat direction. After adding mass terms for vector fields and integrating out heavy degrees of freedom, we also determine the dynamically generated superpotentials in the Nf \le 4 quantum theories. We close with some remarks regarding magnetic duals to the Nf \ge 7 electric SO(11) theories.Comment: 16 pages, harvmac and tables macro

Duality and Dynamical Supersymmetry Breaking in Spin(10)Spin(10) with a Spinor

We study ${\cal N}=1$ supersymmetric $Spin(10)$ chiral gauge theories with a single spinor representation and $N$ vector representations. We present a dual description in terms of an ${\cal N}=1$ supersymmetric $SU(N-5)$ chiral gauge theory with a symmetric tensor, one fundamental and $N$ antifundamental representations. The $Spin(10)$ theory with $N=0$ breaks supersymmetry at strong coupling; we study how this arises at weak coupling in the dual theory, which is a spontaneously broken gauge theory. Also, we recover various known dualities, find new dual pairs and generate new examples of dynamical supersymmetry breaking.Comment: 9 pages, uses harvmac, no figur

The FDA Food Safety and Modernization Act and the Exemption for Small Firms

The FDA Food Safety Modernization Act of 2010 is new legislation that mandates, among other things, new food safety standards. The act includes a clause that exempts small firms from new regulatory requirements. This paper investigates the effects of a small firm exemption from more stringent food safety standards. The model compares food safety, total output and the number of market participants for different food safety regulation with and without an exemption for small firms. The numerical examples show that a more stringent food safety regulation increases food safety, increases the price of food, decreases the total output and decreases the number of firms. A new food safety standard with an exemption for small firms increases the average food safety but not as much as with a new standard alone. An exemption for small firms causes the total number of firms to increase.Food safety, heterogeneous firms, regulation, regulatory exemption, Agricultural and Food Policy, Food Consumption/Nutrition/Food Safety, D21, M31, Q10, Q18,

Supersymmetry Breaking and Duality in SU(N)xSU(N-M) Theories

We consider a class of N=1 supersymmetric Yang-Mills theories, with gauge group SU(N)xSU(N - M) and fundamental matter content. Duality plays an essential role in analyzing the nonperturbative infrared dynamics of these models. We find that Yukawa couplings drive these theories into the confining phase, and show how the nonperturbative superpotentials arise in the dual picture. We show that the odd-N, M = 2 models with an appropriate tree-level superpotential break supersymmetry.Comment: 12p., LaTeX; some typos corrected, version to appear in Phys. Lett.

Welfare Effects of Mandatory Traceability When Firms are Heterogeneous

We develop a framework in which the cost of producing a quantity food and the cost of food safety differs across firms. We show that large firms may supply the safest food even though small firms have a cost advantage in producing safe food. The model shows that mandatory traceability can decrease the overall safety of food when small firms that supply the safest food exit the industry. Our model applies to food safety but can be applied to a wide range of issues related to regulation and product quality.Food safety, quality, traceability, regulation, Industrial Organization, Marketing, Production Economics, D21, L11, L15, Q10,

U-statistic Type Tests for Structural Breaks in Linear Regression Models

This article introduces a U-statistic type process that is based on a kernel function which can depend on nuisance parameters. It is shown here that this process can accommodate very easily anti-symmetric kernels very useful for detecting changing patterns in the dynamics of time series. This theory is applied to structural break hypothesis tests in linear regression models. In particular, the flexibility of these processes will be exploited to introduce a simultaneous and joint test that exhibit statistical power against changes in either intercept or slope. In contrast to the literature, these tests are able to distinguish between rejections due to changes in intercept from rejections due to changes in slope; allow control of global errors rate; and are explicitly designed to have power when the distribution error is asymmetric. These tests can also incorporate different weight functions devised to detect changes early as well as later on in the sample, and show very good performance in small samples. These tests, therefore, outperform CUSUM type tests widely employed in this literature

Patterns of Duality in N=1 SUSY Gauge Theories

We study the patterns in the duality of a wide class of N=1 supersymmetric gauge theories in four dimensions. We present many new generalizations of the classic duality models of Kutasov and Schwimmer, which have themselves been generalized numerous times in works of Intriligator, Leigh and the present authors. All of these models contain one or two fields in a two-index tensor representation, along with fields in the defining representation. The superpotential for the two-index tensor(s) resembles A_k or D_k singularity forms, generalized from numbers to matrices. Looking at the ensemble of these models, classifying them by superpotential, gauge group, and ``level'' -- for terminology we appeal to the architecture of a typical European-style theatre -- we identify emerging patterns and note numerous interesting puzzles.Comment: 34 pages, 4 figures, uses harvmac and table