arXiv subjects

Paul de Medeiros

Publications and source records attributed to Paul de Medeiros.

At least 19 recordsLinked to original sources

arXiv2024

Poincaré superalgebras and triple systems

We consider a class of Poincaré superalgebras for which the nested bracket of three supercharges is necessarily zero only in dimensions greater than three. In lower dimensions, we give a precise characterisation of the data which encodes any such Poincaré superalgebra in terms of a more elementary embedding superalgebra. Up to isomorphism, we classify every classical embedding superalgebra that defines a Poincaré superalgebra. More generally, we show how to construct an embedding superalgebra in dimensions one, two and three from a certain type of triple system whose product structure encodes the nested bracket of three supercharges in the associated Poincaré superalgebra.

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arXiv2024

Applied User Research in Virtual Reality: Tools, Methods, and Challenges

This chapter explores the practice of conducting user research studies and design assessments in virtual reality (VR). An overview of key VR hardware and software tools is provided, including game engines, such as Unity and Unreal Engine. Qualitative and quantitative research methods, along with their various synergies with VR, are likewise discussed, and some of the challenges associated with VR, such as limited sensory stimulation, are reflected upon. VR is proving particularly useful in the context of space systems development, where its utilisation offers a cost-effective and secure method for simulating extraterrestrial environments, allowing for rapid prototyping and evaluation of innovative concepts under representative operational conditions. To illustrate this, we present a case study detailing the application of VR to aid aerospace engineers testing their ideas with end-users and stakeholders during early design stages of the European Space Agency's (ESA) prospective Argonaut lunar lander. This case study demonstrates the effectiveness of VR simulations in gathering important feedback concerning the operability of the Argonaut lander in poor lighting conditions as well as surfacing relevant ergonomics considerations and constraints. The chapter concludes by discussing the strengths and weaknesses associated with VR-based user studies and proposes future research directions, emphasising the necessity for novel VR interfaces to overcome existing technical limitations.

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arXiv2024

Designing for Human Operations on the Moon: Challenges and Opportunities of Navigational HUD Interfaces

Future crewed missions to the Moon will face significant environmental and operational challenges, posing risks to the safety and performance of astronauts navigating its inhospitable surface. Whilst head-up displays (HUDs) have proven effective in providing intuitive navigational support on Earth, the design of novel human-spaceflight solutions typically relies on costly and time-consuming analogue deployments, leaving the potential use of lunar HUDs largely under-explored. This paper explores an alternative approach by simulating navigational HUD concepts in a high-fidelity Virtual Reality (VR) representation of the lunar environment. In evaluating these concepts with astronauts and other aerospace experts (n=25), our mixed methods study demonstrates the efficacy of simulated analogues in facilitating rapid design assessments of early-stage HUD solutions. We illustrate this by elaborating key design challenges and guidelines for future lunar HUDs. In reflecting on the limitations of our approach, we propose directions for future design exploration of human-machine interfaces for the Moon.

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arXiv2023

Using Virtual Reality to Shape Humanity's Return to the Moon: Key Takeaways from a Design Study

Revived interest in lunar exploration is heralding a new generation of design solutions in support of human operations on the Moon. While space system design has traditionally been guided by prototype deployments in analogue studies, the resource-intensive nature of this approach has largely precluded application of proficient user-centered design (UCD) methods from human-computer interaction (HCI). This paper explores possible use of Virtual Reality (VR) to simulate analogue studies in lab settings and thereby bring to bear UCD in this otherwise engineering-dominated field. Drawing on the ongoing development of the European Large Logistics Lander, we have recreated a prospective lunar operational scenario in VR and evaluated it with a group of astronauts and space experts (n=20). Our qualitative findings demonstrate the efficacy of VR in facilitating UCD, enabling efficient contextual inquiries and improving project team coordination. We conclude by proposing future directions to further exploit VR in lunar systems design.

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arXiv2022

Using Virtual Reality to Design and Evaluate a Lunar Lander: The EL3 Case Study

The European Large Logistics Lander (EL3) is being designed to carry out cargo delivery missions in support of future lunar ground crews. The capacity of virtual reality (VR) to visualize and interactively simulate the unique lunar environment makes it a potentially powerful design tool during the early development stages of such solutions. Based on input from the EL3 development team, we have produced a VR-based operational scenario featuring a hypothetical configuration of the lander. Relying on HCI research methods, we have subsequently evaluated this scenario with relevant experts (n=10). Qualitative findings from this initial pilot study have demonstrated the usefulness of VR as a design tool in this context, but likewise surfaced a number of limitations in the form of potentially impaired validity and generalizability. We conclude by outlining our future research plan and reflect on the potential use of physical stimuli to improve the validity of VR-based simulations in forthcoming design activities.

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arXiv2018

Killing superalgebras for Lorentzian six-manifolds

We calculate the Spencer cohomology of the $(1,0)$ Poincaré superalgebras in six dimensions: with and without R-symmetry. As the cases of four and eleven dimensions taught us, we may read off from this calculation a Killing spinor equation which allows the determination of which geometries admit rigidly supersymmetric theories in this dimension. We prove that the resulting Killing spinors generate a Lie superalgebra and determine the geometries admitting the maximal number of such Killing spinors. They are divided in two branches. One branch consists of the lorentzian Lie groups with bi-invariant metrics and, as a special case, it includes the lorentzian Lie groups with a self-dual Cartan three-form which define the maximally supersymmetric backgrounds of $(1,0)$ Poincaré supergravity in six dimensions. The notion of Killing spinor on the other branch does not depend on the choice of a three-form but rather on a one-form valued in the R-symmetry algebra. In this case, we obtain three different (up to local isometry) maximally supersymmetric backgrounds, which are distinguished by the causal type of the one-form.

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arXiv2016

Killing superalgebras for Lorentzian four-manifolds

We determine the Killing superalgebras underpinning field theories with rigid unextended supersymmetry on Lorentzian four-manifolds by re-interpreting them as filtered deformations of $\mathbb{Z}$-graded subalgebras with maximum odd dimension of the $N{=}1$ Poincaré superalgebra in four dimensions. Part of this calculation involves computing a Spencer cohomology group which, by analogy with a similar result in eleven dimensions, prescribes a notion of Killing spinor, which we identify with the defining condition for bosonic supersymmetric backgrounds of minimal off-shell supergravity in four dimensions. We prove that such Killing spinors always generate a Lie superalgebra, and that this Lie superalgebra is a filtered deformation of a subalgebra of the $N{=}1$ Poincaré superalgebra in four dimensions. Demanding the flatness of the connection defining the Killing spinors, we obtain equations satisfied by the maximally supersymmetric backgrounds. We solve these equations, arriving at the classification of maximally supersymmetric backgrounds whose associated Killing superalgebras are precisely the filtered deformations we classify in this paper.

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arXiv2016

Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions

We consider bosonic supersymmetric backgrounds of ten-dimensional conformal supergravity. Up to local conformal isometry, we classify the maximally supersymmetric backgrounds, determine their conformal symmetry superalgebras and show how they arise as near-horizon geometries of certain half-BPS backgrounds or as a plane-wave limit thereof. We then show how to define Yang-Mills theory with rigid supersymmetry on any supersymmetric conformal supergravity background and, in particular, on the maximally supersymmetric backgrounds. We conclude by commenting on a striking resemblance between the supersymmetric backgrounds of ten-dimensional conformal supergravity and those of eleven-dimensional Poincaré supergravity.

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arXiv2014

Submaximal conformal symmetry superalgebras for Lorentzian manifolds of low dimension

We consider a class of smooth oriented Lorentzian manifolds in dimensions three and four which admit a nowhere vanishing conformal Killing vector and a closed two-form that is invariant under the Lie algebra of conformal Killing vectors. The invariant two-form is constrained in a particular way by the conformal geometry of the manifold. In three dimensions, the conformal Killing vector must be everywhere causal (or null if the invariant two-form vanishes identically). In four dimensions, the conformal Killing vector must be everywhere null and the invariant two-form vanishes identically if the geometry is everywhere of Petrov type N or O. To the conformal class of any such geometry, it is possible to assign a particular Lie superalgebra structure, called a conformal symmetry superalgebra. The even part of this superalgebra contains conformal Killing vectors and constant R-symmetries while the odd part contains (charged) twistor spinors. The largest possible dimension of a conformal symmetry superalgebra is realised only for geometries that are locally conformally flat. We determine precisely which non-trivial conformal classes of metrics admit a conformal symmetry superalgebra with the next largest possible dimension, and compute all the associated submaximal conformal symmetry superalgebras. In four dimensions, we also compute symmetry superalgebras for a class of Ricci-flat Lorentzian geometries not of Petrov type N or O which admit a null Killing vector.

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arXiv2014

Superconformal quantum field theory in curved spacetime

By conformally coupling vector and hyper multiplets in Minkowski space, we obtain a class of field theories with extended rigid conformal supersymmetry on any Lorentzian four-manifold admitting twistor spinors. We construct the conformal symmetry superalgebras which describe classical symmetries of these theories and derive an appropriate BRST operator in curved spacetime. In the process, we elucidate the general framework of cohomological algebra which underpins the construction. We then consider the corresponding perturbative quantum field theories. In particular, we examine the conditions necessary for conformal supersymmetries to be preserved at the quantum level, i.e. when the BRST operator commutes with the perturbatively defined S-matrix, which ensures superconformal invariance of amplitudes. To this end, we prescribe a renormalization scheme for time-ordered products that enter the perturbative S-matrix and show that such products obey certain Ward identities in curved spacetime. These identities allow us to recast the problem in terms of the cohomology of the BRST operator. Through a careful analysis of this cohomology, and of the renormalization group in curved spacetime, we establish precise criteria which ensure that all conformal supersymmetries are preserved at the quantum level. As a by-product, we provide a rigorous proof that the beta-function for such theories is one-loop exact. We also briefly discuss the construction of chiral rings and the role of non-perturbative effects in curved spacetime.

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arXiv2013

Conformal symmetry superalgebras

We show how the rigid conformal supersymmetries associated with a certain class of pseudo-Riemannian spin manifolds define a Lie superalgebra. The even part of this superalgebra contains conformal isometries and constant R-symmetries. The odd part is generated by twistor spinors valued in a particular R-symmetry representation. We prove that any manifold which admits a conformal symmetry superalgebra of this type must generically have dimension less than seven. Moreover, in dimensions three, four, five and six, we provide the generic data from which the conformal symmetry superalgebra is prescribed. For conformally flat metrics in these dimensions, and compact R-symmetry, we identify each of the associated conformal symmetry superalgebras with one of the conformal superalgebras classified by Nahm. We also describe several examples for Lorentzian metrics that are not conformally flat.

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arXiv2012

Rigid supersymmetry, conformal coupling and twistor spinors

We investigate the relationship between conformal and spin structure on lorentzian manifolds and see how their compatibility influences the formulation of rigid supersymmetric field theories. In dimensions three, four, six and ten, we show that if the Dirac current associated with a generic spinor defines a null conformal Killing vector then the spinor must obey a twistor equation with respect to a certain connection with torsion. Of the theories we consider, those with classical superconformal symmetry in Minkowski space can be reformulated as rigid supersymmetric theories on any lorentzian manifold admitting twistor spinors. In dimensions six and ten, we also describe rigid supersymmetric gauge theories on bosonic minimally supersymmetric supergravity backgrounds.

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arXiv2011

On the structure of quadrilateral brane tilings

Brane tilings provide the most general framework in string and M-theory for matching toric Calabi-Yau singularities probed by branes with superconformal fixed points of quiver gauge theories. The brane tiling data consists of a bipartite tiling of the torus which encodes both the classical superpotential and gauge-matter couplings for the quiver gauge theory. We consider the class of tilings which contain only tiles bounded by exactly four edges and present a method for generating any tiling within this class by iterating combinations of certain graph-theoretic moves. In the context of D3-branes in IIB string theory, we consider the effect of these generating moves within the corresponding class of supersymmetric quiver gauge theories in four dimensions. Of particular interest are their effect on the superpotential, the vacuum moduli space and the conditions necessary for the theory to reach a superconformal fixed point in the infrared. We discuss the general structure of physically admissible quadrilateral brane tilings and Seiberg duality in terms of certain composite moves within this class.

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arXiv2010

Eulerian digraphs and toric Calabi-Yau varieties

We investigate the structure of a simple class of affine toric Calabi-Yau varieties that are defined from quiver representations based on finite eulerian directed graphs (digraphs). The vanishing first Chern class of these varieties just follows from the characterisation of eulerian digraphs as being connected with all vertices balanced. Some structure theory is used to show how any eulerian digraph can be generated by iterating combinations of just a few canonical graph-theoretic moves. We describe the effect of each of these moves on the lattice polytopes which encode the toric Calabi-Yau varieties and illustrate the construction in several examples. We comment on physical applications of the construction in the context of moduli spaces for superconformal gauged linear sigma models.

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arXiv2010

Half-BPS M2-brane orbifolds

Smooth Freund-Rubin backgrounds of eleven-dimensional supergravity of the form AdS_4 x X^7 and preserving at least half of the supersymmetry have been recently classified. Requiring that amount of supersymmetry forces X to be a spherical space form, whence isometric to the quotient of the round 7-sphere by a freely-acting finite subgroup of SO(8). The classification is given in terms of ADE subgroups of the quaternions embedded in SO(8) as the graph of an automorphism. In this paper we extend this classification by dropping the requirement that the background be smooth, so that X is now allowed to be an orbifold of the round 7-sphere. We find that if the background preserves more than half of the supersymmetry, then it is automatically smooth in accordance with the homogeneity conjecture, but that there are many half-BPS orbifolds, most of them new. The classification is now given in terms of pairs of ADE subgroups of quaternions fibred over the same finite group. We classify such subgroups and then describe the resulting orbifolds in terms of iterated quotients. In most cases the resulting orbifold can be described as a sequence of cyclic quotients.

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arXiv2009

Half-BPS quotients in M-theory: ADE with a twist

We classify Freund-Rubin backgrounds of eleven-dimensional supergravity of the form AdS_4 x X^7 which are at least half BPS; equivalently, smooth quotients of the round 7-sphere by finite subgroups of SO(8) which admit an (N>3)-dimensional subspace of Killing spinors. The classification is given in terms of pairs consisting of an ADE subgroup of SU(2) and an automorphism defining its embedding in SO(8). In particular we find novel half-BPS quotients associated with the subgroups of type D_n (for n>5), E_7 and E_8 and their outer automorphisms.

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arXiv2009

Superpotentials for superconformal Chern-Simons theories from representation theory

These notes provide a detailed account of the universal structure of superpotentials defining a large class of superconformal Chern-Simons theories with matter, many of which appear as the low-energy descriptions of multiple M2-brane configurations. The amount of superconformal symmetry in the Chern-Simons-matter theory determines the minimum amount of global symmetry that the associated quartic superpotential must realise, which in turn restricts the matter superfield representations. Our analysis clarifies the necessary representation-theoretic data which guarantees a particular amount of superconformal symmetry. Thereby we shall recover all the examples of M2-brane effective field theories that have appeared in the recent literature. The results are based on a refinement of the unitary representation theory of Lie algebras to the case when the Lie algebra admits an ad-invariant inner product. The types of representation singled out by the superconformal symmetry turn out to be intimately associated with triple systems admitting embedding Lie (super)algebras and we obtain a number of new results about these triple systems which might be of independent interest. In particular, we prove that any metric 3-Lie algebra embeds into a real metric 3-graded Lie superalgebra in such a way that the 3-bracket is given by a nested Lie bracket.

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arXiv2009

Metric 3-Lie algebras for unitary Bagger-Lambert theories

We prove a structure theorem for finite-dimensional indefinite-signature metric 3-Lie algebras admitting a maximally isotropic centre. This algebraic condition indicates that all the negative-norm states in the associated Bagger-Lambert theory can be consistently decoupled from the physical Hilbert space. As an immediate application of the theorem, new examples beyond index 2 are constructed. The lagrangian for the Bagger-Lambert theory based on a general physically admissible 3-Lie algebra of this kind is obtained. Following an expansion around a suitable vacuum, the precise relationship between such theories and certain more conventional maximally supersymmetric gauge theories is found. These typically involve particular combinations of N=8 super Yang-Mills and massive vector supermultiplets. A dictionary between the 3-Lie algebraic data and the physical parameters in the resulting gauge theories will thereby be provided.

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