A Note on T-dualities in the Pure Spinor Heterotic String

In this note we study the preservation of the classical pure spinor BRST constraints under super T-duality transformations. We also determine the invariance of the one-loop conformal invariance and of the local gauge and Lorentz anomalies under the super Tdualities

A Very Brief Introduction to Machine Learning With Applications to Communication Systems

Given the unprecedented availability of data and computing resources, there is widespread renewed interest in applying data-driven machine learning methods to problems for which the development of conventional engineering solutions is challenged by modelling or algorithmic deficiencies. This tutorial-style paper starts by addressing the questions of why and when such techniques can be useful. It then provides a high-level introduction to the basics of supervised and unsupervised learning. For both supervised and unsupervised learning, exemplifying applications to communication networks are discussed by distinguishing tasks carried out at the edge and at the cloud segments of the network at different layers of the protocol stack

The Non-minimal Heterotic Pure Spinor String in a Curved Background

We study the non-minimal pure spinor string in a curved background. We find that the minimal BRST invariance implies the existence of a non-trivial stress-energy tensor for the minimal and non-minimal variables in the heterotic curved background. We find constraint equations for the b ghost. We construct the b ghost as a solution of these constraints.Comment: 14 pages, harvmac big. Typos corrected. Minor changes, appendix adde

General fluctuations of the heterotic pure spinor string on curved backgrounds

The general fluctuations, in the form of vertex operators, for the heterotic superstring in the pure spinor formalism are considered. The case of a flat background is reviewed and the case of a curved case is studied. The left-moving ghosts are pure spinors and the right-moving ghosts come from fixing the reparametrization invariance. The role of the reparametrization ghosts in the construction of the vertex operators is emphasized.Comment: 11 pages, harvmac big. Corrections and reference adde