Resolution of Infrared Divergences in Gluon-Gluon Scattering Regulated on a Lightcone Worldsheet Lattice

We improve and update the discussion, given some years ago by my collaborators and me, of infrared divergences and Bremsstrahlung in one-loop gluon scattering probabilities in lightcone gauge. In that work, we showed that adding soft and collinear gluon radiation, satisfying simple Lorentz invariant constraints, not only cancelled all IR divergences, but resulted in compact expressions for the consequent scattering probabilities. Here we impose less restrictive (albeit noncovariant) constraints on the unobserved radiation, which increases the high energy (s) fixed momentum transfer (t) behavior of the total probabilities from -ln^2s to ln s ln t, a behavior shared by the (IR divergent) elastic probabilities. Using this new treatment we also make a much more detailed comparison of the lightcone results to covariant calculations using dimensional regularization, finding complete agreement between the two styles of calculation.Comment: 14 pages, 1 figur

Digitizing the Neveu-Schwarz Model on the Lightcone Worldsheet

The purpose of this article is to extend the lightcone worldsheet lattice description of string theory to include the Neveu-Schwarz model. We model each component of the fermionic worldsheet field by a critical Ising model. We show that a simple choice of boundary conditions for the Ising variables leads to the half integer modes required by the model. We identify the G-parity operation within the Ising model and formulate the procedure for projecting onto the even G-parity sector. We construct the lattice version of the three open string vertex, with the necessary operator insertion at the interaction point. We sketch a formalism for summing planar open string multi-loop amplitudes, and we discuss prospects for numerically summing them. If successful, the methods described here could provide an alternative to lattice gauge theory for computations in large N QCD.Comment: 23 pages, 7 figure

1/N Perturbations in Superstring Bit Models

We develop the 1/N expansion for stable string bit models, focusing on a model with bit creation operators carrying only transverse spinor indices a=1,...,s. At leading order (1/N=0), this model produces a (discretized) lightcone string with a "transverse space' of $s$ Grassmann worldsheet fields. Higher orders in the 1/N expansion are shown to be determined by the overlap of a single large closed chain (discretized string) with two smaller closed chains. In the models studied here, the overlap is not accompanied with operator insertions at the break/join point. Then the requirement that the discretized overlap have a smooth continuum limit leads to the critical Grassmann "dimension" of s=24. This "protostring", a Grassmann analog of the bosonic string, is unusual, because it has no large transverse dimensions. It is a string moving in one space dimension and there are neither tachyons nor massless particles. The protostring, derived from our pure spinor string bit model, has 24 Grassmann dimensions, 16 of which could be bosonized to form 8 compactified bosonic dimensions, leaving 8 Grassmann dimensions--the worldsheet content of the superstring. If the transverse space of the protostring could be "decompactified", string bit models might provide an appealing and solid foundation for superstring theory.Comment: 26 page

Phonetic drift

This chapter provides an overview of research on the phonetic changes that occur in one’s native language (L1) due to recent experience in another language (L2), a phenomenon known as phonetic drift. Through a survey of empirical findings on segmental and suprasegmental acoustic properties, the chapter examines the features of the L1 that are subject to phonetic drift, the cognitive mechanism(s) behind phonetic drift, and the various factors that influence the likelihood of phonetic drift. In short, virtually all aspects of L1 speech are subject to drift, but different aspects do not drift in the same manner, possibly due to multiple routes of L2 influence coexisting at different levels of L1 phonological structure. In addition to the timescale of these changes, the chapter discusses the relationship between phonetic drift and attrition as well as some of the enduring questions in this area.https://drive.google.com/open?id=1eQbh17Z4YsH8vY_XjCHGqi5QChfBKcAZhttps://drive.google.com/open?id=1eQbh17Z4YsH8vY_XjCHGqi5QChfBKcAZhttps://drive.google.com/open?id=1eQbh17Z4YsH8vY_XjCHGqi5QChfBKcAZAccepted manuscriptAccepted manuscrip

Space from String Bits

We develop superstring bit models, in which the lightcone transverse coordinates in D spacetime dimensions are replaced with d=D-2 double-valued "flavor" indices $x^k-> f_k=1,2$; $k=2,...,d+1$. In such models the string bits have no space to move. Letting each string bit be an adjoint of a "color" group U(N), we then analyze the physics of 't Hooft's limit $N->\infty$, in which closed chains of many string bits behave like free lightcone IIB superstrings with d compact coordinate bosonic worldsheet fields $x^k$, and s pairs of Grassmann fermionic fields $\theta_{L,R}^a$, a=1,..., s. The coordinates $x^k$ emerge because, on the long chains, flavor fluctuations enjoy the dynamics of d anisotropic Heisenberg spin chains. It is well-known that the low energy excitations of a many-spin Heisenberg chain are identical to those of a string worldsheet coordinate compactified on a circle of radius $R_k$, which is related to the anisotropy parameter $-1<\Delta_k<1$ of the corresponding Heisenberg system. Furthermore there is a limit of this parameter, $\Delta_k->\pm 1$, in which $R_k->\infty$. As noted in earlier work [Phys.Rev.D{\bf 89}(2014)105002], these multi-string-bit chains are strictly stable at $N=\infty$ when d<s and only marginally stable when d=s. (Poincare supersymmetry requires d=s=8, which is on the boundary between stability and instability.)Comment: 22 pages, several typos correcte

Determinants for the Lightcone Worldsheet

The evaluation of the determinant of the Laplacian defined on two dimensional regions of various shapes is an essential ingredient in calculating the scattering amplitudes of strings. In lightcone parameterization the regions are rectangular in shape with several slits of different length and location cut parallel to the $\tau$ axis of the rectangle. This paper offers a compendium of applications of the methods of Kac and McKean and Singer to the calculation of such worldsheet determinants. Particular attention is paid to the effect of corners on the determinants. The effect of corners joining edges with like boundary conditions is implicit in Kac's results. We discuss the generalization to a corner joining a Dirichlet edge to a Neumann edge, and apply it to a scattering amplitude involving D-branes.Comment: 36 pages, 5 figures, references and relevant comments adde