Fivebranes and 4-manifolds

We describe rules for building 2d theories labeled by 4-manifolds. Using the proposed dictionary between building blocks of 4-manifolds and 2d N=(0,2) theories, we obtain a number of results, which include new 3d N=2 theories T[M_3] associated with rational homology spheres and new results for Vafa-Witten partition functions on 4-manifolds. In particular, we point out that the gluing measure for the latter is precisely the superconformal index of 2d (0,2) vector multiplet and relate the basic building blocks with coset branching functions. We also offer a new look at the fusion of defect lines / walls, and a physical interpretation of the 4d and 3d Kirby calculus as dualities of 2d N=(0,2) theories and 3d N=2 theories, respectivelyComment: 81 pages, 18 figures. v2: misprints corrected, clarifications and references added. v3: additions and corrections about lens space theory, 4-manifold gluing, smooth structure

A Class of Topological Actions

We review definitions of generalized parallel transports in terms of Cheeger-Simons differential characters. Integration formulae are given in terms of Deligne-Beilinson cohomology classes. These representations of parallel transport can be extended to situations involving distributions as is appropriate in the context of quantized fields.Comment: 41 pages, no figure

Super-A-polynomials for Twist Knots

We conjecture formulae of the colored superpolynomials for a class of twist knots $K_p$ where p denotes the number of full twists. The validity of the formulae is checked by applying differentials and taking special limits. Using the formulae, we compute both the classical and quantum super-A-polynomial for the twist knots with small values of p. The results support the categorified versions of the generalized volume conjecture and the quantum volume conjecture. Furthermore, we obtain the evidence that the Q-deformed A-polynomials can be identified with the augmentation polynomials of knot contact homology in the case of the twist knots.Comment: 22+16 pages, 16 tables and 5 figures; with a Maple program by Xinyu Sun and a Mathematica notebook in the ancillary files linked on the right; v2 change in appendix B, typos corrected and references added; v3 change in section 3.3; v4 corrections in Ooguri-Vafa polynomials and quantum super-A-polynomials for 7_2 and 8_1 are adde

Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams

We show how Feynman amplitudes of standard QFT on flat and homogeneous space can naturally be recast as the evaluation of observables for a specific spin foam model, which provides dynamics for the background geometry. We identify the symmetries of this Feynman graph spin foam model and give the gauge-fixing prescriptions. We also show that the gauge-fixed partition function is invariant under Pachner moves of the triangulation, and thus defines an invariant of four-dimensional manifolds. Finally, we investigate the algebraic structure of the model, and discuss its relation with a quantization of 4d gravity in the limit where the Newton constant goes to zero.Comment: 28 pages (RevTeX4), 7 figures, references adde

Dichromatic state sum models for four-manifolds from pivotal functors

A family of invariants of smooth, oriented four-dimensional manifolds is defined via handle decompositions and the Kirby calculus of framed link diagrams. The invariants are parametrised by a pivotal functor from a spherical fusion category into a ribbon fusion category. A state sum formula for the invariant is constructed via the chain-mail procedure, so a large class of topological state sum models can be expressed as link invariants. Most prominently, the Crane-Yetter state sum over an arbitrary ribbon fusion category is recovered, including the nonmodular case. It is shown that the Crane-Yetter invariant for nonmodular categories is stronger than signature and Euler invariant. A special case is the four-dimensional untwisted Dijkgraaf-Witten model. Derivations of state space dimensions of TQFTs arising from the state sum model agree with recent calculations of ground state degeneracies in Walker-Wang models. Relations to different approaches to quantum gravity such as Cartan geometry and teleparallel gravity are also discussed

An Invitation to Higher Gauge Theory

In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge '2-group'. We focus on 6 examples. First, every abelian Lie group gives a Lie 2-group; the case of U(1) yields the theory of U(1) gerbes, which play an important role in string theory and multisymplectic geometry. Second, every group representation gives a Lie 2-group; the representation of the Lorentz group on 4d Minkowski spacetime gives the Poincar\'e 2-group, which leads to a spin foam model for Minkowski spacetime. Third, taking the adjoint representation of any Lie group on its own Lie algebra gives a 'tangent 2-group', which serves as a gauge 2-group in 4d BF theory, which has topological gravity as a special case. Fourth, every Lie group has an 'inner automorphism 2-group', which serves as the gauge group in 4d BF theory with cosmological constant term. Fifth, every Lie group has an 'automorphism 2-group', which plays an important role in the theory of nonabelian gerbes. And sixth, every compact simple Lie group gives a 'string 2-group'. We also touch upon higher structures such as the 'gravity 3-group' and the Lie 3-superalgebra that governs 11-dimensional supergravity.Comment: 60 pages, based on lectures at the 2nd School and Workshop on Quantum Gravity and Quantum Geometry at the 2009 Corfu Summer Institut

The L&E of Intellectual Property – Do we get maximum innovation with the current regime?

Innovation is crucial to economic growth – the essential path for lifting much of the world population out of dire poverty and for maintaining the living standard of those who already have. To stimulate innovation, the legal system has to support the means through which innovators seek to get rewarded for their efforts. Amongst these means, some, such as the first mover advantage or 'lead time,' are not directly legal; but secrets and intellectual property rights are legal institutions supported for the specific purpose of stimulating innovation. Whilst the protection of secrets has not changed very much over recent years, intellectual property (or IP) has. IP borrows some features from ordinary property rights, but is also distinct, in that, unlike physical goods, information, the object of IP, is not inherently scarce; indeed as information and communication technologies expand, the creation and distribution of information is becoming ever cheaper and in many circumstances abundant, so that selection is of the essence ('on the internet, point of view is everything'). Where rights on information extend too far, their monopolising effect may hamper innovation. The paper investigates the underlying structure of IP rights and surveys what we know empirically about the incentive effects of IP as about industries that flourish without formal IP

The Supermembrane with Central Charges on a G2 Manifold

We construct the 11D supermembrane with topological central charges induced through an irreducible winding on a G2 manifold realized from the T7/Z2xZ2xZ2 orbifold construction. The hamiltonian H of the theory on a T7 target has a discrete spectrum. Within the discrete symmetries of H associated to large diffeomorphisms, the Z2xZ2xZ2 group of automorphisms of the quaternionic subspaces preserving the octonionic structure is relevant. By performing the corresponding identification on the target space, the supermembrane may be formulated on a G2 manifold, preserving the discretness of its supersymmetric spectrum. The corresponding 4D low energy effective field theory has N=1 supersymmetry.Comment: Reviewed version. spectral propertis discussed, two more sections added, 27 pages,Late

Non-invasive cardiac assessment in high risk patients (The GROUND study): rationale, objectives and design of a multi-center randomized controlled clinical trial

Background: Peripheral arterial disease (PAD) is a common disease associated with a considerably increased risk of future cardiovascular events and most of these patients will die from coronary artery disease (CAD). Screening for silent CAD has become an option with recent non-invasive developments in CT (computed tomography)-angiography and MR (magnetic resonance) stress testing. Screening in combination with more aggressive treatment may improve prognosis. Therefore we propose to study whether a cardiac imaging algorithm, using non-invasive imaging techniques followed by treatment will reduce the risk of cardiovascular disease in PAD patients free from cardiac symptoms. Design: The GROUND study is designed as a prospective, multi-center, randomized clinical trial. Patients with peripheral arterial disease, but without symptomatic cardiac disease will be asked to participate. All patients receive a proper risk factor management before randomization. Half of the recruited patients will enter the 'control group' and only undergo CT calcium scoring. The other half of the recruited patients (index group) will undergo the non invasive cardiac imaging algorithm followed by evidence-based treatment. First, patients are submitted to CT calcium scoring and CT angiography. Patients with a left main (or equivalent) coronary artery stenosis of > 50% on CT will be referred to a cardiologist without further imaging. All other patients in this group will undergo dobutamine stress magnetic resonance (DSMR) testing. Patients with a DSMR positive for ischemia will also be referred to a cardiologist. These patients are candidates for conventional coronary angiography and cardiac interventions (coronary artery bypass grafting (CABG) or percutaneous cardiac interventions (PCI)), if indicated. All participants of the trial will enter a 5 year follow up period for the occurrence of cardiovascular events. Sequential interim analysis will take place. Based on sample size calculations about 1200 patients are needed to detect a 24% reduction in primary outcome. Implications: The GROUND study will provide insight into the question whether non-invasive cardiac imaging reduces the risk of cardiovascular events in patients with peripheral arterial disease, but without symptoms of coronary artery disease. Trial registration: Clinicaltrials.gov NCT0018911