BPS States of Exceptional Non-Critical Strings

We study the BPS states of non-critical strings which arise for zero size instantons of exceptional groups. This is accomplished by using F-theory and M-theory duals and by employing mirror symmetry to compute the degeneracy of membranes wrapped around 2-cycles of the Calabi-Yau threefold. We find evidence for a number of novel physical phenomena, including having infinitely many light states with the first lightest state including a nearly massless gravitino.Comment: 29 pages, 1 figure, references added, to appear in the proceedings of the conference "Advanced Quantum Field Theory'' (in memory of Claude Itzykson

Concept talk cannot be avoided

Distinct systems for representing concepts as prototypes, exemplars, and theories are closely integrated in the mind, and the notion of concept is required as a framework for exploring this integration. Eliminating the term “concept” from our theories will hinder rather than promote scientific progress

K3--Fibrations and Heterotic-Type II String Duality

We analyze the map between heterotic and type II N=2 supersymmetric string theories for certain two and three moduli examples found by Kachru and Vafa. The appearance of elliptic j-functions can be traced back to specializations of the Picard-Fuchs equations to systems for $K_3$ surfaces. For the three-moduli example we write the mirror maps and Yukawa couplings in the weak coupling limit in terms of j-functions; the expressions agree with those obtained in perturbative calculations in the heterotic string in an impressive way. We also discuss symmetries of the world-sheet instanton numbers in the type II theory, and interpret them in terms of S--duality of the non-perturbative heterotic string.Comment: 16p, harvmac with hyperlink