Three-dimensional (p,q) AdS superspaces and matter couplings

We introduce N-extended (p,q) AdS superspaces in three space-time dimensions, with p+q=N and p>=q, and analyse their geometry. We show that all (p,q) AdS superspaces with X^{IJKL}=0 are conformally flat. Nonlinear sigma-models with (p,q) AdS supersymmetry exist for p+q4 the target space geometries are highly restricted). Here we concentrate on studying off-shell N=3 supersymmetric sigma-models in AdS_3. For each of the cases (3,0) and (2,1), we give three different realisations of the supersymmetric action. We show that (3,0) AdS supersymmetry requires the sigma-model to be superconformal, and hence the corresponding target space is a hyperkahler cone. In the case of (2,1) AdS supersymmetry, the sigma-model target space must be a non-compact hyperkahler manifold endowed with a Killing vector field which generates an SO(2) group of rotations of the two-sphere of complex structures.Comment: 52 pages; V3: minor corrections, version published in JHE

Extended supersymmetric sigma models in AdS_4 from projective superspace

There exist two superspace approaches to describe N=2 supersymmetric nonlinear sigma models in four-dimensional anti-de Sitter (AdS_4) space: (i) in terms of N=1 AdS chiral superfields, as developed in arXiv:1105.3111 and arXiv:1108.5290; and (ii) in terms of N=2 polar supermultiplets using the AdS projective-superspace techniques developed in arXiv:0807.3368. The virtue of the approach (i) is that it makes manifest the geometric properties of the N=2 supersymmetric sigma-models in AdS_4. The target space must be a non-compact hyperkahler manifold endowed with a Killing vector field which generates an SO(2) group of rotations on the two-sphere of complex structures. The power of the approach (ii) is that it allows us, in principle, to generate hyperkahler metrics as well as to address the problem of deformations of such metrics. Here we show how to relate the formulation (ii) to (i) by integrating out an infinite number of N=1 AdS auxiliary superfields and performing a superfield duality transformation. We also develop a novel description of the most general N=2 supersymmetric nonlinear sigma-model in AdS_4 in terms of chiral superfields on three-dimensional N=2 flat superspace without central charge. This superspace naturally originates from a conformally flat realization for the four-dimensional N=2 AdS superspace that makes use of Poincare coordinates for AdS_4. This novel formulation allows us to uncover several interesting geometric results.Comment: 88 pages; v3: typos corrected, version published in JHE

Scalable and Interpretable One-class SVMs with Deep Learning and Random Fourier features

One-class support vector machine (OC-SVM) for a long time has been one of the most effective anomaly detection methods and extensively adopted in both research as well as industrial applications. The biggest issue for OC-SVM is yet the capability to operate with large and high-dimensional datasets due to optimization complexity. Those problems might be mitigated via dimensionality reduction techniques such as manifold learning or autoencoder. However, previous work often treats representation learning and anomaly prediction separately. In this paper, we propose autoencoder based one-class support vector machine (AE-1SVM) that brings OC-SVM, with the aid of random Fourier features to approximate the radial basis kernel, into deep learning context by combining it with a representation learning architecture and jointly exploit stochastic gradient descent to obtain end-to-end training. Interestingly, this also opens up the possible use of gradient-based attribution methods to explain the decision making for anomaly detection, which has ever been challenging as a result of the implicit mappings between the input space and the kernel space. To the best of our knowledge, this is the first work to study the interpretability of deep learning in anomaly detection. We evaluate our method on a wide range of unsupervised anomaly detection tasks in which our end-to-end training architecture achieves a performance significantly better than the previous work using separate training.Comment: Accepted at European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML-PKDD) 201

N = 2 supersymmetric sigma-models and duality

For two families of four-dimensional off-shell N = 2 supersymmetric nonlinear sigma-models constructed originally in projective superspace, we develop their formulation in terms of N = 1 chiral superfields. Specifically, these theories are: (i) sigma-models on cotangent bundles T*M of arbitrary real analytic Kaehler manifolds M; (ii) general superconformal sigma-models described by weight-one polar supermultiplets. Using superspace techniques, we obtain a universal expression for the holomorphic symplectic two-form \omega^{(2,0)} which determines the second supersymmetry transformation and is associated with the two complex structures of the hyperkaehler space T*M that are complimentary to the one induced from M. This two-form is shown to coincide with the canonical holomorphic symplectic structure. In the case (ii), we demonstrate that \omega^{(2,0)} and the homothetic conformal Killing vector determine the explicit form of the superconformal transformations. At the heart of our construction is the duality (generalized Legendre transform) between off-shell N = 2 supersymmetric nonlinear sigma-models and their on-shell N = 1 chiral realizations. We finally present the most general N = 2 superconformal nonlinear sigma-model formulated in terms of N = 1 chiral superfields. The approach developed can naturally be generalized in order to describe 5D and 6D superconformal nonlinear sigma-models in 4D N = 1 superspace.Comment: 31 pages, no figures; V2: reference and comments added, typos corrected; V3: more typos corrected, published versio

Classification of non-Riemannian doubled-yet-gauged spacetime

Assuming $\mathbf{O}(D,D)$ covariant fields as the `fundamental' variables, Double Field Theory can accommodate novel geometries where a Riemannian metric cannot be defined, even locally. Here we present a complete classification of such non-Riemannian spacetimes in terms of two non-negative integers, $(n,\bar{n})$, $0\leq n+\bar{n}\leq D$. Upon these backgrounds, strings become chiral and anti-chiral over $n$ and $\bar{n}$ directions respectively, while particles and strings are frozen over the $n+\bar{n}$ directions. In particular, we identify $(0,0)$ as Riemannian manifolds, $(1,0)$ as non-relativistic spacetime, $(1,1)$ as Gomis-Ooguri non-relativistic string, $(D{-1},0)$ as ultra-relativistic Carroll geometry, and $(D,0)$ as Siegel's chiral string. Combined with a covariant Kaluza-Klein ansatz which we further spell, $(0,1)$ leads to Newton-Cartan gravity. Alternative to the conventional string compactifications on small manifolds, non-Riemannian spacetime such as $D=10$, $(3,3)$ may open a new scheme of the dimensional reduction from ten to four.Comment: 1+41 pages; v2) Refs added; v3) Published version; v4) Sign error in (2.51) correcte

Off-shell superconformal nonlinear sigma-models in three dimensions

We develop superspace techniques to construct general off-shell N=1,2,3,4 superconformal sigma-models in three space-time dimensions. The most general N=3 and N=4 superconformal sigma-models are constructed in terms of N=2 chiral superfields. Several superspace proofs of the folklore statement that N=3 supersymmetry implies N=4 are presented both in the on-shell and off-shell settings. We also elaborate on (super)twistor realisations for (super)manifolds on which the three-dimensional N-extended superconformal groups act transitively and which include Minkowski space as a subspace.Comment: 67 pages; V2: typos corrected, one reference added, version to appear on JHE

Physiotherapy, and speech and language therapy intervention for patients with refractory chronic cough: a multicentre randomised control trial.

BACKGROUND: Physiotherapy, and speech and language therapy are emerging non-pharmacological treatments for refractory chronic cough. We aimed to investigate the efficacy of a physiotherapy, and speech and language therapy intervention (PSALTI) to improve health-related quality of life (HRQoL) and to reduce cough frequency in patients with refractory chronic cough. METHODS: In this multicentre randomised controlled trial, patients with refractory chronic cough were randomised to four weekly 1:1 sessions of either PSALTI consisting of education, laryngeal hygiene and hydration, cough suppression techniques, breathing exercises and psychoeducational counselling or control intervention consisting of healthy lifestyle advice. We assessed the change in HRQoL at week 4 with the Leicester Cough Questionnaire (LCQ). Secondary efficacy outcomes included 24-hour objective cough frequency (Leicester Cough Monitor) and cough reflex sensitivity. The primary analysis used an analysis of covariance adjusted for baseline measurements with the intention-to-treat population. This study was registered at UK Clinical Research Network (UKCRN ID 10678). FINDINGS: Between December 2011 and April 2014, we randomly assigned 75 participants who underwent baseline assessment (34 PSALTI and 41 controls). In the observed case analysis, HRQoL (LCQ) improved on average by 1.53 (95% CI 0.21 to 2.85) points more in PSALTI group than with control (p=0.024). Cough frequency decreased by 41% (95% CI 36% to 95%) in PSALTI group relative to control (p=0.030). The improvements within the PSALTI group were sustained up to 3 months. There was no significant difference between groups in the concentration of capsaicin causing five or more coughs. INTERPRETATION: Greater improvements in HRQoL and cough frequency were observed with PSALTI intervention. Our findings support the use of PSALTI for patients with refractory chronic cough. TRIAL REGISTRATION NUMBER: UKCRN ID 10678 and ISRCTN 73039760; Results

On duality symmetry in perturbative quantum theory

Non-compact symmetries of extended 4d supergravities involve duality rotations of vectors and thus are not manifest off-shell invariances in standard "second-order" formulation. To study how such symmetries are realised in the quantum theory we consider examples in 2 dimensions where vector-vector duality is replaced by scalar-scalar one. Using a "doubled" formulation, where fields and their momenta are treated on an equal footing and the duality becomes a manifest symmetry of the action (at the expense of Lorentz symmetry), we argue that the corresponding on-shell quantum effective action or S-matrix are duality symmetric as well as Lorentz invariant. The simplest case of discrete Z_2 duality corresponds to a symmetry of the S-matrix under flipping the sign of the negative-chirality scalars in 2 dimensions or phase rotations of chiral (definite-helicity) parts of vectors in 4 dimensions. We also briefly discuss some 4d models and comment on implications of our analysis for extended supergravities.Comment: 21 pages, Latex v2: comments and references added v3: references and minor comments adde

Global Symmetries and D-Terms in Supersymmetric Field Theories

We study the role of D-terms in supersymmetry (SUSY) breaking. By carefully analyzing the SUSY multiplets containing various conserved currents in theories with global symmetries, we obtain a number of constraints on the renormalization group flow in supersymmetric field theories. Under broad assumptions, these results imply that there are no SUSY-breaking vacua, not even metastable ones, with parametrically large D-terms. This explains the absence of such D-terms in models of dynamical SUSY-breaking. There is, however, a rich class of calculable models which generate comparable D-terms and F-terms through a variety of non-perturbative effects; these D-terms can be non-abelian. We give several explicit examples of such models, one of which is a new calculable limit of the 3-2 model.Comment: 34 pages, 2 figures; reference added, minor change

Bottom mixed layer oxygen dynamics in the Celtic Sea

The seasonally stratified continental shelf seas are highly productive, economically important environments which are under considerable pressure from human activity. Global dissolved oxygen concentrations have shown rapid reductions in response to anthropogenic forcing since at least the middle of the twentieth century. Oxygen consumption is at the same time linked to the cycling of atmospheric carbon, with oxygen being a proxy for carbon remineralisation and the release of CO2. In the seasonally stratified seas the bottom mixed layer (BML) is partially isolated from the atmosphere and is thus controlled by interplay between oxygen consumption processes, vertical and horizontal advection. Oxygen consumption rates can be both spatially and temporally dynamic, but these dynamics are often missed with incubation based techniques. Here we adopt a Bayesian approach to determining total BML oxygen consumption rates from a high resolution oxygen time-series. This incorporates both our knowledge and our uncertainty of the various processes which control the oxygen inventory. Total BML rates integrate both processes in the water column and at the sediment interface. These observations span the stratified period of the Celtic Sea and across both sandy and muddy sediment types. We show how horizontal advection, tidal forcing and vertical mixing together control the bottom mixed layer oxygen concentrations at various times over the stratified period. Our muddy-sand site shows cyclic spring-neap mediated changes in oxygen consumption driven by the frequent resuspension or ventilation of the seabed. We see evidence for prolonged periods of increased vertical mixing which provide the ventilation necessary to support the high rates of consumption observed