Joel A. Shapiro

Pomeron factorization in general dual models

We demonstrate that in each ghost-free dual model with one minor restriction, there exists a critical dimensionality of space-time in which the pomeron singularity becomes a factorizable Regge pole. In each model when this dimensionality is chosen, the pomeron emerges with twice the intercept and half the slope of the leading secondary (f) trajectory. We explicitly construct the pomeron propagator and the operator coupling the pomeron to the reggeon sector for the general dual model, including the lower-lying negative-G-parity pomeron in the Neveu-Schwarz model. Gauge identities and physical states in the pomeron sector are also investigated. In all of the dual models the pomeron form factors exhibit a generalized f dominance and modified Wu-Yang behavior.

The Nonplanar One Loop Amplitude in Witten's String Field Theory

Abstract We develop methods for calculating the one-open-string-irreducible diagrams for Wittens string field theory. These provide the coefficients for an expansion of the quantum effective action in a power series in the string field Φ. Each external leg of a diagram is labelled by an element of the BRST first-quantized string state space. We choose the standard oscillator Fock states as a convenient basis for this labelling. Our method is to represent each Feynman diagram as a path integral over space-time coordinates xμ and the bosonized world-sheet ghost field φ. The dependence of the diagram on the external strings and ghost insertions is obtained by completing the square. The coefficient of this dependence, the “measure”, is then inferred by exploiting the Weyl invariance of the Polyakov path integrals. As an illustration of our methods, we analyze in detail the one loop nonplanar two string function. This is the simplest diagram containing information on closed strings. Calling pμ the energy-momentum carried by one of the external legs, we find poles in p 2 at −α′p 2 = 1 2 n − 4, with n=0,1,2,… . The pole locations with n≠8k are unphysical and such poles must disappear for physical open string states. We confirm this explicitly for n=1,2 and argue that this decoupling happens generally.

Closed string-open string transitions and witten's string field theory

Abstract Using conformal mapping techniques, we obtain a new BRST invariant operator ϒ encoding in closed form transition amplitudes between open strings and closed strings. The residues of the closed string poles in the non-planar one-loop two-point diagram of Wittens string field theory are finite sums of products of these amplitudes.

Supergravity torsion constraints from the 10D superparticle

Abstract The classical superparticle propagating in a curved superspace is studied. Requiring that there be a local fermionic symmetry imposes restrictions on the background. The equivalence relation among background superfields which is implied by the superparticle dynamics is discussed, and it is shown that up to such equivalences the torsion superfields obey the supergravity constraints.

Superspace supergravity from the superstring

Abstract We study a classical superstring propagating in a “curved” (10,16)-dimensional superspace. In this formulation of the string, a local fermionic symmetry is needed to eliminate ghosts from the particle spectrum. By studying the constraint algebra, we show that any background field configuration consistent with this symmetry is equivalent to one which satisfies the full set of supergravity equations.

The spacetime supersymmetric formulation of the string

Abstract The Green-Schwarz formulation of the ten-dimensional superstring is one of the more intriguing approaches to string theory. Together with the Brink-Schwarz superparticle and the super-p-branes, the Green-Schwarz superstring has both a manifest spacetime supersymmetry and an obscure local worldsheet (worldline, world volume) fermionic symmetry. Preservation of this latter symmetry of the string in the presence of background massless fields implies constraints on these background fields which are equivalent to their classical equations of motion. This correspondence underlies a twistor-like transform in ten dimensions. When formulated in a curved background superspace, the superstring defines an equivalence relation on superspace geometries which explains the equivalence of differing formulations of supergravity in superspace. These developments in classical superobjects are reviewed in this report, and we make some comments on recent progress in their quantization.

A test of the collective field method for the N → ∞ limit

Abstract The collective field method applied to the one-dimensional planar model is shown to give exactly the entire epectrum of SU( N ) symmetric states in the large- N limit.

DETERMINING THE DIMENSIONS OF VARIABLES IN PHYSICS ALGEBRAIC EQUATIONS

This paper describes work on methods that evaluate algebraic solutions to word problems in physics. Many current tutoring systems rely on substantial scaffolding and consequently require students to completely describe every variable used in the solution. A heuristic, based on constraint propagation, capable of inferring the description of variables (i.e., the possible dimensions and physics concepts) is shown to be highly reliable on three real world data sets, one covering a few problems with a small number of student answers and two others covering a large class of problems (~100) with a large number of student answers (~11,000). The heuristic uniquely determines the dimensions of all the variables in 91–92% of the equation sets. By asking the student for dimension information about one variable, an additional 3% of the sets can be determined. An ITS tutoring system can use this heuristic to reason about a students answers even when the scaffolding and context are removed.

Knowledge Based Mechanisms for Tutoring Systems in Science and Engineering

In science and engineering courses, students are often presented a situation for which they are asked to identify the relevant principles and to instantiate them as a set of equations. For an ITS to determine the correctness and relevance of the students answer and generate effective feedback, it must map the student variables and equations onto the physical properties and concepts that are relevant to the situation. The space of possible mappings of variables and equations is extremely large. Domain independent techniques by themselves are unable to overcome the complexity hurdles. This paper describes how an ITS can use constraint propagation and algebraic techniques combined with domain and problem-specific knowledge to solve the mapping problem with systems of algebraic equations. The techniques described in this paper have been implemented in the PHYSICS_TUTOR tutoring system and evaluated on three data sets that contain submissions from students in several introductory Physics courses.

Symplectic Reduction of the Minimally Coupled Massless Superparticle in D=10

In this study of the Brink-Schwarz superparticle in the presence of background non-abelian gauge field, we derive the D=10 super Yang-Mills curvature constraints by demanding an analog of the Siegel supersymmetry. We then show that, assuming F αβ = 0, the twistor transform proposed by Witten can be described using symplectic reduction.