Anomalously light mesons in a (1+1)-dimensional supersymmetric theory with fundamental matter

We consider N=1 supersymmetric Yang-Mills theory with fundamental matter in the large-N_c approximation in 1+1 dimensions. We add a Chern-Simons term to give the adjoint partons a mass and solve for the meson bound states. Here mesons are color-singlet states with two partons in the fundamental representation but are not necessarily bosons. We find that this theory has anomalously light meson bound states at intermediate and strong coupling. We also examine the structure functions for these states and find that they prefer to have as many partons as possible at low longitudinal momentum fraction.Comment: 14 pages, 3 figures, LaTe

A Lower Bound for the First Passage Time Density of the Suprathreshold Ornstein-Uhlenbeck Process

We prove that the first passage time density $\rho(t)$ for an Ornstein-Uhlenbeck process $X(t)$ obeying $dX=-\beta X dt + \sigma dW$ to reach a fixed threshold $\theta$ from a suprathreshold initial condition $x_0>\theta>0$ has a lower bound of the form $\rho(t)>k \exp\left[-p e^{6\beta t}\right]$ for positive constants $k$ and $p$ for times $t$ exceeding some positive value $u$. We obtain explicit expressions for $k, p$ and $u$ in terms of $\beta$, $\sigma$, $x_0$ and $\theta$, and discuss application of the results to the synchronization of periodically forced stochastic leaky integrate-and-fire model neurons.Comment: 15 pages, 1 figur

N=1 super Yang-Mills on a (3+1) dimensional transverse lattice with one exact supersymmetry

We formulate ${\cal N}$=1 super Yang-Mills theory in 3+1 dimensions on a two dimensional transverse lattice using supersymmetric discrete light cone quantization in the large-$N_c$ limit. This formulation is free of fermion species doubling. We are able to preserve one supersymmetry. We find a rich, non-trivial behavior of the mass spectrum as a function of the coupling $g\sqrt{N_c}$, and see some sort of "transition" in the structure of a bound state as we go from the weak coupling to the strong coupling. Using a toy model we give an interpretation of the rich behavior of the mass spectrum. We present the mass spectrum as a function of the winding number for those states whose color flux winds all the way around in one of the transverse directions. We use two fits to the mass spectrum and the one that has a string theory justification appears preferable. For those states whose color flux is localized we present an extrapolated value for $m^2$ for some low energy bound states in the limit where the numerical resolution goes to infinity.Comment: 23(+2 for v3) pages, 19 figures; v2: a footnote added; v3: an appendix, comments, references added. The version to appear PR

Heating Up and Cooling Down: Modifying the Provocation Defense by Expanding Cooling Time

This Note argues for expanding the provocationdefense for criminal defendants by broadening theapplicability and recognition of both cooling time andrekindling. This expansion can be accomplished bytransforming cooling time and rekindling into subjectivestandards that focus on the unique internal and externalqualities of the defendant. Doing so would not only beconsistent with the underlying purpose of the defense butalso appropriate considering our modern understandingof the psychological effects of trauma and reactivity toprovoking stimuli. Accordingly, courts should practiceleniency with respect to cooling time and rekindling. Thebest approach to provocation is one that considers theconcept of cooling time as a means of evaluating the factsand circumstances of the defendant’s situation ratherthan a tool to bar the defense. This Note concludes thatbecause the provocation defense results only inmitigation and not acquittal, courts should abandon thecategorical approach to provocation and the objectivestandard of cooling time altogether to allow forflexibility across individual and cultural contexts

Two-dimensional super Yang-Mills theory investigated with improved resolution

In earlier work, N=(1,1) super Yang--Mills theory in two dimensions was found to have several interesting properties, though these properties could not be investigated in any detail. In this paper we analyze two of these properties. First, we investigate the spectrum of the theory. We calculate the masses of the low-lying states using the supersymmetric discrete light-cone (SDLCQ) approximation and obtain their continuum values. The spectrum exhibits an interesting distribution of masses, which we discuss along with a toy model for this pattern. We also discuss how the average number of partons grows in the bound states. Second, we determine the number of fermions and bosons in the N=(1,1) and N=(2,2) theories in each symmetry sector as a function of the resolution. Our finding that the numbers of fermions and bosons in each sector are the same is part of the answer to the question of why the SDLCQ approximation exactly preserves supersymmetry.Comment: 20 pages, 10 figures, LaTe

(1+1)-Dimensional Yang-Mills Theory Coupled to Adjoint Fermions on the Light Front

We consider SU(2) Yang-Mills theory in 1+1 dimensions coupled to massless adjoint fermions. With all fields in the adjoint representation the gauge group is actually SU(2)/Z_2, which possesses nontrivial topology. In particular, there are two distinct topological sectors and the physical vacuum state has a structure analogous to a \theta vacuum. We show how this feature is realized in light-front quantization, with periodicity conditions used to regulate the infrared and treating the gauge field zero mode as a dynamical quantity. We find expressions for the degenerate vacuum states and construct the analog of the \theta vacuum. We then calculate the bilinear condensate in the model. We argue that the condensate does not affect the spectrum of the theory, although it is related to the string tension that characterizes the potential between fundamental test charges when the dynamical fermions are given a mass. We also argue that this result is fundamentally different from calculations that use periodicity conditions in x^1 as an infrared regulator.Comment: 20 pages, Revte

Effects of a fundamental mass term in two-dimensional super Yang-Mills theory

We show that adding a vacuum expectation value to a gauge field left over from a dimensional reduction of three-dimensional pure supersymmetric Yang-Mills theory generates mass terms for the fundamental fields in the two-dimensional theory while supersymmetry stays intact. This is similar to the adjoint mass term that is generated by a Chern-Simons term in this theory. We study the spectrum of the two-dimensional theory as a function of the vacuum expectation value and of the Chern-Simons coupling. Apart from some symmetry issues a straightforward picture arises. We show that at least one massless state exists if the Chern-Simons coupling vanishes. The numerical spectrum separates into (almost) massless and very heavy states as the Chern-Simons coupling grows. We present evidence that the gap survives the continuum limit. We display structure functions and other properties of some of the bound states.Comment: 17 pp., 10 figs; substantially revised version to be published in Phys. Rev.