Dyons in N=4 Supersymmetric Theories and Three-Pronged Strings

We construct and explore BPS states that preserve 1/4 of supersymmetry in N=4 Yang-Mills theories. Such states are also realized as three-pronged strings ending on D3-branes. We correct the electric part of the BPS equation and relate its solutions to the unbroken abelian gauge group generators. Generic 1/4-BPS solitons are not spherically symmetric, but consist of two or more dyonic components held apart by a delicate balance between static electromagnetic force and scalar Higgs force. The instability previously found in three-pronged string configurations is due to excessive repulsion by one of these static forces. We also present an alternate construction of these 1/4-BPS states from quantum excitations around a magnetic monopole, and build up the supermultiplet for arbitrary (quantized) electric charge. The degeneracy and the highest spin of the supermultiplet increase linearly with a relative electric charge. We conclude with comments.Comment: 33 pages, two figures, LaTex, a footnote added, the figure caption of Fig.2 expanded, one more referenc

Identifying Task Engagement: Towards Personalised Interactions with Educational Robots

Abstract-The focus of this project is to design, develop and evaluate a new computational model for automatically detecting change in task engagement. This work will be applied to robotic tutors to enhance and support the learning experience, enabling timely pedagogical and empathic intervention. This work is intended to forward the current state of the art by 1) exploring how to automatically detect engagement with a learning task, 2) designing and developing new approaches to machine learning for adaptive platform-independent modelling and 3) evaluation of its effectiveness for building and maintaining learner engagement across different tutor embodiments, for example a physical and virtual embodiment

Noncommutative U(1) Instantons in Eight Dimensional Yang-Mills Theory

We study the noncommutative version of the extended ADHM construction in the eight dimensional U(1) Yang-Mills theory. This construction gives rise to the solutions of the BPS equations in the Yang-Mills theory, and these solutions preserve at least 3/16 of supersymmetries. In a wide subspace of the extended ADHM data, we show that the integer $k$ which appears in the extended ADHM construction should be interpreted as the $D4$-brane charge rather than the $D0$-brane charge by explicitly calculating the topological charges in the case that the noncommutativity parameter is anti-self-dual. We also find the relationship with the solution generating technique and show that the integer $k$ can be interpreted as the charge of the $D0$-brane bound to the $D8$-brane with the $B$-field in the case that the noncommutativity parameter is self-dual.Comment: 22 page

Calorons, Nahm's equations on S^1 and bundles over P^1xP^1

The moduli space of solutions to Nahm's equations of rank (k,k+j) on the circle, and hence, of SU(2) calorons of charge (k,j), is shown to be equivalent to the moduli of holomorphic rank 2 bundles on P^1xP^1 trivialized at infinity with c_2=k and equipped with a flag of degree j along P^1x{0}. An explicit matrix description of these spaces is given by a monad constructio

Gravitating monopoles in SU(3) gauge theory

We consider the Einstein-Yang-Mills-Higgs equations for an SU(3) gauge group in a spherically symmetric ansatz. Several properties of the gravitating monopole solutions are obtained an compared with their SU(2) counterpart.Comment: 7 pages, Latex, 3 figure

Prochlo: Strong Privacy for Analytics in the Crowd

The large-scale monitoring of computer users' software activities has become commonplace, e.g., for application telemetry, error reporting, or demographic profiling. This paper describes a principled systems architecture---Encode, Shuffle, Analyze (ESA)---for performing such monitoring with high utility while also protecting user privacy. The ESA design, and its Prochlo implementation, are informed by our practical experiences with an existing, large deployment of privacy-preserving software monitoring. (cont.; see the paper

SU(5) monopoles and non-abelian black holes

We construct spherically and axially symmetric monopoles in SU(5) Yang-Mills-Higgs theory both in flat and curved space as well as spherical and axial non-abelian, ''hairy'' black holes. We find that in analogy to the SU(2) case, the flat space monopoles are either non-interacting (in the BPS limit) or repelling. In curved space, however, gravity is able to overcome the repulsion for suitable choices of the Higgs coupling constants and the gravitational coupling. In addition, we confirm that indeed all qualitative features of (gravitating) SU(2) monopoles are found as well in the SU(5) case. For the non-abelian black holes, we compare the behaviour of the solutions in the BPS limit with that for non-vanishing Higgs self-coupling constants.Comment: 14 Revtex pages, 9 PS-figure

Axially Symmetric Monopoles and Black Holes in Einstein-Yang-Mills-Higgs Theory

We investigate static axially symmetric monopole and black hole solutions with magnetic charge n > 1 in Einstein-Yang-Mills-Higgs theory. For vanishing and small Higgs selfcoupling, multimonopole solutions are gravitationally bound. Their mass per unit charge is lower than the mass of the n=1 monopole. For large Higgs selfcoupling only a repulsive phase exists. The static axially symmetric hairy black hole solutions possess a deformed horizon with constant surface gravity. We consider their properties in the isolated horizon framework, interpreting them as bound states of monopoles and black holes. Representing counterexamples to the ``no-hair'' conjecture, these black holes are neither uniquely characterized by their horizon area and horizon charge.Comment: 23 Revtex pages, 43 Postscript figure