Orientifold planes, affine algebras and magnetic monopoles

We analyze string theory backgrounds that include different kinds of orientifold planes and map out a natural correspondence to (twisted) affine Kac-Moody algebras. The low-energy description of specific BPS states in these backgrounds leads to a construction of explicit twisted magnetic monopole solutions on R^3 x S^1. These backgrounds yield new low-energy field theories with twisted boundary conditions and the link with affine algebras yields a natural guess for the superpotentials of the corresponding pure N=1, and N=1* gauge theories.Comment: 23 pages, 7 figures, references adde

Codimension-3 Singularities and Yukawa Couplings in F-theory

F-theory is one of the frameworks where all the Yukawa couplings of grand unified theories are generated and their computation is possible. The Yukawa couplings of charged matter multiplets are supposed to be generated around codimension-3 singularity points of a base complex 3-fold, and that has been confirmed for the simplest type of codimension-3 singularities in recent studies. However, the geometry of F-theory compactifications is much more complicated. For a generic F-theory compactification, such issues as flux configuration around the codimension-3 singularities, field-theory formulation of the local geometry and behavior of zero-mode wavefunctions have virtually never been addressed before. We address all these issues in this article, and further discuss nature of Yukawa couplings generated at such singularities. In order to calculate the Yukawa couplings of low-energy effective theory, however, the local descriptions of wavefunctions on complex surfaces and a global characterization of zero-modes over a complex curve have to be combined together. We found the relation between them by re-examining how chiral charged matters are characterized in F-theory compactification. An intrinsic definition of spectral surfaces in F-theory turns out to be the key concept. As a biproduct, we found a new way to understand the Heterotic--F theory duality, which improves the precision of existing duality map associated with codimension-3 singularities.Comment: 91 pages; minor clarification, typos corrected and a reference added (v3

Worldvolume Theories, Holography, Duality and Time

Duality transformations involving compactifications on timelike as well as spacelike circles link M-theory, the 10+1-dimensional strong coupling limit of IIA string theory, to other 11-dimensional theories in signatures 9+2 and 6+5 and to type II string theories in all 10-dimensional signatures. These theories have BPS branes of various world-volume signatures, and here we construct the world-volume theories for these branes, which in each case have 16 supersymmetries. For the generalised D-branes of the various type II string theories, these are always supersymmetric Yang-Mills theories with 16 supersymmetries, and we show that these all arise from compactifications of the supersymmetric Yang-Mills theories in 9+1 or 5+5 dimensions. We discuss the geometry of the brane solutions and, for the cases in which the world-volume theories are superconformally invariant, we propose holographically dual string or M theories in constant curvature backgrounds. For product space solutions $X\times Y$, there is in general a conformal field theory associated with the boundary of $X$ and another with the boundary of $Y$.Comment: 35 pages, harvma

New Dimensions for Wound Strings: The Modular Transformation of Geometry to Topology

We show, using a theorem of Milnor and Margulis, that string theory on compact negatively curved spaces grows new effective dimensions as the space shrinks, generalizing and contextualizing the results in hep-th/0510044. Milnor's theorem relates negative sectional curvature on a compact Riemannian manifold to exponential growth of its fundamental group, which translates in string theory to a higher effective central charge arising from winding strings. This exponential density of winding modes is related by modular invariance to the infrared small perturbation spectrum. Using self-consistent approximations valid at large radius, we analyze this correspondence explicitly in a broad set of time-dependent solutions, finding precise agreement between the effective central charge and the corresponding infrared small perturbation spectrum. This indicates a basic relation between geometry, topology, and dimensionality in string theory.Comment: 28 pages, harvmac big. v2: references and KITP preprint number added, minor change

Cavitation Inside Enlarged And Real-Size Fully Transparent Injector Nozzles And Its Effect On Near Nozzle Spray Formation

The effect of string cavitation in various transparent Diesel injector nozzles on near nozzle spray dispersion angle is examined. Additional PDA measurements on spray characteristics produced from real-size transparent nozzle tips are presented. Highspeed imaging has provided qualitative information on the existence of geometric and string cavitation, simultaneously with the temporal variation of the spray angle. Additional use of commercial and in-house developed CFD models has provided complimentary information on the local flow field. Results show that there is strong connection between string cavitation structures and spray instabilities. Moreover, elimination of string cavitation results in a stable spray shape that is only controlled by the extent of geometric-induced cavitation pockets. Finally, PDA measurements on real-size transparent nozzle tips have confirmed that such nozzles reproduce successfully the sprays generated by production metal nozzles

Supersymmetry Enhancement and Junctions in S-folds

We study supersymmetry enhancement from ${\cal N}=3$ to ${\cal N}=4$ proposed by Aharony and Tachikawa by using string junctions in S-folds. The central charges carried by junctions play a central role in our analysis. We consider planer junctions in a specific plane. Before the S-folding they carry two complex central charges, which we denote by $Z$ and $\bar Z$. The S-fold projection eliminates $\bar Z$ as well as one of the four supercharges, and when the supersymmetry is enhanced $\bar Z$ should be reproduced by some non-perturbative mechanism. For the models of $\mathbb{Z}_3$ and $\mathbb{Z}_4$ S-folds which are expected to give $SU(3)$ and $SO(5)$ ${\cal N}=4$ theories we compare the junction spectra with those in perturbative brane realization of the same theories. We establish one-to-one correspondence so that $Z$ coincides. By using the correspondence we also give an expression for the enhanced central charge $\bar Z$.Comment: 30 pages, 7 figures, v2: minor corrections, version accepted for publication in JHE

Computing Covers Using Prefix Tables

An \emph{indeterminate string} $x = x[1..n]$ on an alphabet $\Sigma$ is a sequence of nonempty subsets of $\Sigma$; $x$ is said to be \emph{regular} if every subset is of size one. A proper substring $u$ of regular $x$ is said to be a \emph{cover} of $x$ iff for every $i \in 1..n$, an occurrence of $u$ in $x$ includes $x[i]$. The \emph{cover array} $\gamma = \gamma[1..n]$ of $x$ is an integer array such that $\gamma[i]$ is the longest cover of $x[1..i]$. Fifteen years ago a complex, though nevertheless linear-time, algorithm was proposed to compute the cover array of regular $x$ based on prior computation of the border array of $x$. In this paper we first describe a linear-time algorithm to compute the cover array of regular string $x$ based on the prefix table of $x$. We then extend this result to indeterminate strings.Comment: 14 pages, 1 figur