The Quantum Dynamics of Heterotic Vortex Strings

We study the quantum dynamics of vortex strings in N=1 SQCD with U(N_c) gauge group and N_f=N_c quarks. The classical worldsheet of the string has N=(0,2) supersymmetry, but this is broken by quantum effects. We show how the pattern of supersymmetry breaking and restoration on the worldsheet captures the quantum dynamics of the underlying 4d theory. We also find qualitative matching of the meson spectrum in 4d and the spectrum on the worldsheet.Comment: 13 page

Instanton Effects in Three-Dimensional Supersymmetric Gauge Theories with Matter

Using standard field theory techniques we compute perturbative and instanton contributions to the Coulomb branch of three-dimensional supersymmetric QCD with N=2 and N=4 supersymmetry and gauge group SU(2). For the N=4 theory with one massless flavor, we confirm the proposal of Seiberg and Witten that the Coulomb branch is the double-cover of the centered moduli space of two BPS monopoles constructed by Atiyah and Hitchin. Introducing a hypermultiplet mass term, we show that the asymptotic metric on the Coulomb branch coincides with the metric on Dancer's deformation of the monopole moduli space. For the N=2 theory with $N_f$ flavors, we compute the one-loop corrections to the metric and complex structure on the Coulomb branch. We then determine the superpotential including one-loop effects around the instanton background. These calculations provide an explicit check of several results previously obtained by symmetry and holomorphy arguments.Comment: 24 pages, Late

Ordered fast fourier transforms on a massively parallel hypercube multiprocessor

Design alternatives for ordered Fast Fourier Transformation (FFT) algorithms were examined on massively parallel hypercube multiprocessors such as the Connection Machine. Particular emphasis is placed on reducing communication which is known to dominate the overall computing time. To this end, the order and computational phases of the FFT were combined, and the sequence to processor maps that reduce communication were used. The class of ordered transforms is expanded to include any FFT in which the order of the transform is the same as that of the input sequence. Two such orderings are examined, namely, standard-order and A-order which can be implemented with equal ease on the Connection Machine where orderings are determined by geometries and priorities. If the sequence has N = 2 exp r elements and the hypercube has P = 2 exp d processors, then a standard-order FFT can be implemented with d + r/2 + 1 parallel transmissions. An A-order sequence can be transformed with 2d - r/2 parallel transmissions which is r - d + 1 fewer than the standard order. A parallel method for computing the trigonometric coefficients is presented that does not use trigonometric functions or interprocessor communication. A performance of 0.9 GFLOPS was obtained for an A-order transform on the Connection Machine

Multilingual Training and Cross-lingual Adaptation on CTC-based Acoustic Model

Multilingual models for Automatic Speech Recognition (ASR) are attractive as they have been shown to benefit from more training data, and better lend themselves to adaptation to under-resourced languages. However, initialisation from monolingual context-dependent models leads to an explosion of context-dependent states. Connectionist Temporal Classification (CTC) is a potential solution to this as it performs well with monophone labels. We investigate multilingual CTC in the context of adaptation and regularisation techniques that have been shown to be beneficial in more conventional contexts. The multilingual model is trained to model a universal International Phonetic Alphabet (IPA)-based phone set using the CTC loss function. Learning Hidden Unit Contribution (LHUC) is investigated to perform language adaptive training. In addition, dropout during cross-lingual adaptation is also studied and tested in order to mitigate the overfitting problem. Experiments show that the performance of the universal phoneme-based CTC system can be improved by applying LHUC and it is extensible to new phonemes during cross-lingual adaptation. Updating all the parameters shows consistent improvement on limited data. Applying dropout during adaptation can further improve the system and achieve competitive performance with Deep Neural Network / Hidden Markov Model (DNN/HMM) systems on limited data

Superconformal Vortex Strings

We study the low-energy dynamics of semi-classical vortex strings living above Argyres-Douglas superconformal field theories. The worldsheet theory of the string is shown to be a deformation of the CP^N model which flows in the infra-red to a superconformal minimal model. The scaling dimensions of chiral primary operators are determined and the dimensions of the associated relevant perturbations on the worldsheet and in the four dimensional bulk are found to agree. The vortex string thereby provides a map between the A-series of N=2 superconformal theories in two and four dimensions.Comment: 22 pages. v2: change to introductio

Heterotic Vortex Strings

We determine the low-energy N=(0,2) worldsheet dynamics of vortex strings in a large class of non-Abelian N=1 supersymmetric gauge theories.Comment: 44 pages, 3 figures. v2: typos corrected, reference adde

Phase diagram of the frustrated Hubbard model

The Mott-Hubbard metal-insulator transition in the paramagnetic phase of the one-band Hubbard model has long been used to describe similar features in real materials like V$_2$O$_3$. Here we show that this transition is hidden inside a rather robust antiferromagnetic insulator even in the presence of comparatively strong magnetic frustration. This result raises the question of the relevance of the Mott-Hubbard metal-insulator transition for the generic phase diagram of the one-band Hubbard model.Comment: 4 pages, 6 figure

D-Branes in Field Theory

Certain gauge theories in four dimensions are known to admit semi-classical D-brane solitons. These are domain walls on which vortex flux tubes may end. The purpose of this paper is to develop an open-string description of these D-branes. The dynamics of the domain walls is shown to be governed by a Chern-Simons-Higgs theory which, at the quantum level, captures the classical "closed string" scattering of domain wall solitons.Comment: 23 Pages, 3 figures. v2: reference adde