Conformal Fixed Points of Unidentified Gauge Theories

In this article we discuss gauge/strings correspondence based on the non-critical strings. With this goal we present several remarkable sigma models with the AdS target spaces. The models have kappa symmetry and are completely integrable. The radius of the AdS space is fixed and thus they describe isolated fixed points of gauge theories in various dimensionsComment: 14 page

On the direct indecomposability of infinite irreducible Coxeter groups and the Isomorphism Problem of Coxeter groups

In this paper we prove, without the finite rank assumption, that any irreducible Coxeter group of infinite order is directly indecomposable as an abstract group. The key ingredient of the proof is that we can determine, for an irreducible Coxeter group, the centralizers of the normal subgroups that are generated by involutions. As a consequence, we show that the problem of deciding whether two general Coxeter groups are isomorphic, as abstract groups, is reduced to the case of irreducible Coxeter groups, without assuming the finiteness of the number of the irreducible components or their ranks. We also give a description of the automorphism group of a general Coxeter group in terms of those of its irreducible components.Comment: 30 page

A Geometric Representation for the Proca Model

The Proca model is quantized in an open-path dependent representation that generalizes the Loop Representation of gauge theories. The starting point is a gauge invariant Lagrangian that reduces to the Proca Lagrangian when certain gauge is selected.Comment: 10 pages, Late

Maximally Supersymmetric Yang-Mills in five dimensions in light-cone superspace

We formulate maximally supersymmetric Yang-Mills theory in five dimensions in light-cone superspace. The light-cone Hamiltonian is of the quadratic form and the theory can be understood as an oxidation of the N=4 Super Yang-Mills Theory in four dimensions. We specifically study three-point counterterms and show how these counterterms vanish on-shell. This study is a preliminary to set up the technique in order to study possible four-point counterterms.Comment: 25 pages, typos corrected, references adde

Grading Injustice: Initial Appearance Report Cards

Arrested people across the United States often wait in jail for days, weeks, or even months before seeing a judge or meeting an attorney. In November 2021, the Deason Criminal Justice Reform Center published Ending Injustice: Solving the Initial Appearance Crisis, a comprehensive report about this ongoing crisis in pre-trial due process. That report described the devastating consequences of delayed and uncounseled initial appearances. Now, these Initial Appearance Report Cards offer a closer look at the laws governing post-arrest procedures in each U.S. state, the District of Columbia, Guam, Puerto Rico, and the U.S. Virgin Islands. While the Deason Center’s previous report provided an overview of the initial appearance crisis nationwide, the Initial Appearance Report Cards are a rigorous assessment of the laws in almost every jurisdiction in the country. These report cards reveal enormous gaps in the legal protections accorded to people accused of crimes, illuminating both the scope of the initial appearance crisis and our urgent need to solve it.https://scholar.smu.edu/deasoncenter/1008/thumbnail.jp

How to Solve the Initial Appearance Crisis

Across the United States, people are arrested and held behind bars for days, weeks, and sometimes even months, without ever seeing a judge or attorney. These delays violate the United States Constitution’s promise that an arrested person—who is innocent unless proven guilty—will have prompt access to the courts, the assistance of counsel, and a fair and speedy trial. These due process milestones begin at initial appearance: the first time an arrested person sees a judge about their case. At an initial appearance, the judge should inform an arrested person of the charges against them. The judge should also make an informed decision about whether, and under what conditions, to release a person from jail pending trial. The judge should hold this initial appearance promptly after arrest, and an attorney should advocate for the arrested person. Too often, none of these things happen. This policy brief outlines five best legal practices for jurisdictions to honor the United States Constitution and protect the rights of all arrested people. In addition to detailing each best practice, the publication outlines strategies for success that jurisdictions can use when implementing these vital policies.https://scholar.smu.edu/deasoncenter/1010/thumbnail.jp

Anatomy of neck configuration in fission decay

The anatomy of neck configuration in the fission decay of Uranium and Thorium isotopes is investigated in a microscopic study using Relativistic mean field theory. The study includes $^{236}U$ and $^{232}Th$ in the valley of stability and exotic neutron rich isotopes $^{250}U$, $^{256}U$, $^{260}U$, $^{240}Th$, $^{250}Th$, $^{256}Th$ likely to play important role in the r-process nucleosynthesis in stellar evolution. Following the static fission path, the neck configurations are generated and their composition in terms of the number of neutrons and protons are obtained showing the progressive rise in the neutron component with the increase of mass number. Strong correlation between the neutron multiplicity in the fission decay and the number of neutrons in the neck is seen. The maximum neutron-proton ratio is about 5 for $^{260}$U and $^{256}$Th suggestive of the break down of liquid-drop picture and inhibition of the fission decay in still heavier isotopes. Neck as precursor of a new mode of fission decay like multi-fragmentation fission may also be inferred from this study.Comment: 16 pages, 5 figures (Accepted

N=8 Supergravity 4-point Amplitudes

We present the explicit expressions in N=8 supergravity for the bosonic 4-particle tree and 1-loop amplitudes including vectors and scalars. We also present the candidate 4-point UV divergences in a form of helicity amplitudes, corresponding to 3-loop manifestly N=8 supersymmetric and Lorentz covariant counterterm. This may shed some light on the 3-loop finiteness of N=8 SG and on a conjectured higher loop finiteness. We perform a supersymmetric deformation to complex momentum of the 4-point generating function including higher-loop counterterms and the 1-loop UV finite amplitudes. Using the explicit form of the scalar part of the 3-loop counterterm and of the 1-loop UV finite scalar 4-point amplitudes we find that they both have an unbroken E7 symmetry. We derive from E7 symmetry the low-energy theorem for the 1-loop n-point amplitudes.Comment: 23 p, 4 figure

Noncommutative Superspace, N=1/2 Supersymmetry, Field Theory and String Theory

We deform the standard four dimensional $\N=1$ superspace by making the odd coordinates $\theta$ not anticommuting, but satisfying a Clifford algebra. Consistency determines the other commutation relations of the coordinates. In particular, the ordinary spacetime coordinates $x$ cannot commute. We study chiral superfields and vector superfields and their interactions. As in ordinary noncommutative field theory, a change of variables allows us to express the gauge interactions in terms of component fields which are subject to standard gauge transformation laws. Unlike ordinary noncommutative field theories, the change of the Lagrangian is a polynomial in the deformation parameter. Despite the deformation, the noncommutative theories still have an antichiral ring with all its usual properties. We show how these theories with precisely this deformation arise in string theory in a graviphoton background.Comment: 19 page

From lightcone actions to maximally supersymmetric amplitudes

In this article actions for N=4 SYM and N=8 supergravity are formulated in terms of a chiral superfield, which contains only the physical degrees of freedom of either theory. In these new actions, which originate from the lightcone superspace, the supergravity cubic vertex is the square of the gauge theory one (omitting the color structures). Amplitude calculations using the corresponding Feynman supergraph rules are tedious, but can be simplified by choosing a preferred superframe. Recursive calculations of all MHV amplitudes in N=4 SYM and the four-point N=8 supergravity amplitude are shown to agree with the known results and connections to the BCFW recursion relations are pointed out. Finally, the new path integrals are discussed in the context of the double-copy property relating N=4 SYM theory to N=8 supergravity.Comment: 29 pages, 2 figures, v2: title modified, published versio