Wall Crossing from Dirac Zeromodes

We explore the physics of two-body decay of BPS states using semiclassical analysis to construct explicit solutions that illustrate the main features of wall crossing, for both ordinary and framed BPS states. In particular we recover the primitive wall-crossing formula from an asymptotic analysis of certain Dirac-type operators on monopole moduli spaces. Along the way we give an asymptotic metric for the moduli space of singular monopoles, analogous to the Gibbons-Manton and Lee-Weinberg-Yi metrics for the moduli space of smooth monopoles, and we find evidence for the existence of stable non-BPS boundstates. Our discussion applies to four-dimensional N = 2 super-Yang-Mills theories with general gauge group and general 't Hooft defects.Comment: 32 pages plus appendices; 1 figure. v2: references added, typos fixed. v3: references added, published versio

Spectral networks

We introduce new geometric objects called spectral networks. Spectral networks are networks of trajectories on Riemann surfaces obeying certain local rules. Spectral networks arise naturally in four-dimensional N=2 theories coupled to surface defects, particularly the theories of class S. In these theories spectral networks provide a useful tool for the computation of BPS degeneracies: the network directly determines the degeneracies of solitons living on the surface defect, which in turn determine the degeneracies for particles living in the 4d bulk. Spectral networks also lead to a new map between flat GL(K,C) connections on a two-dimensional surface C and flat abelian connections on an appropriate branched cover Sigma of C. This construction produces natural coordinate systems on moduli spaces of flat GL(K,C) connections on C, which we conjecture are cluster coordinate systems.Comment: 87 pages, 48 figures; v2: typos, correction to general rule for signs of BPS count

Sample preference for colorectal cancer screening tests: blood or stool?

Objective: Despite the high prevalence of CRC and the proven benefits of faecal sampling tests, participation rates in CRC screening are suboptimal. Literature has identified a number of barriers to participation, including faecal aversion. Emerging test technologies suggest blood-based molecular markers might provide an alternative, more acceptable option, for CRC screening tests. We aim to determine preference for blood compared to faeces as the sample for the screening test. Methods: A survey was mailed to 956 South Australians aged 50 to 74 years. Data were collected on sample preference, demographic variables, and ratings of screening test convenience and comfort. Results: The survey yielded a 43% response rate. The majority of participants preferred to provide a blood sample (78% v 22%, p < 0.001). Women were more likely to prefer blood than men (82% vs 74%, p = 0.05). Sample experience influenced preferences, with a significantly higher preference for faeces among participants with experience in faecal sampling (27% vs 17% with no experience, p < 0.05). Participants who preferred to provide a faecal sample rated it significantly more convenient (p < 0.001), more comfortable (p < 0.001), and more acceptable (p < 0.001) than those who preferred blood sampling. Conclusions: Survey participants overwhelmingly indicate a preference for the idea of a blood sample over a faecal sample for CRC screening. Preference was influenced by gender, experience with sampling method and the individual’s perception of sampling convenience, sampling comfort and sample acceptability. Our results suggest population participation rates are likely to improve with blood-based screening tests.Joanne M. Osborne, Carlene Wilson, Vivienne Moore, Tess Gregory, Ingrid Flight, Graeme P. Youn

Kondo Effect in Electromigrated Gold Break Junctions

We present gate-dependent transport measurements of Kondo impurities in bare gold break junctions, generated with high yield using an electromigration process that is actively controlled. Thirty percent of measured devices show zero-bias conductance peaks. Temperature dependence suggests Kondo temperatures \~7K. The peak splitting in magnetic field is consistent with theoretical predictions for g=2, though in many devices the splitting is offset from 2guB by a fixed energy. The Kondo resonances observed here may be due to atomic-scale metallic grains formed during electromigration.Comment: 5 pages, 3 figure

Wall-Crossing in Coupled 2d-4d Systems

We introduce a new wall-crossing formula which combines and generalizes the Cecotti-Vafa and Kontsevich-Soibelman formulas for supersymmetric 2d and 4d systems respectively. This 2d-4d wall-crossing formula governs the wall-crossing of BPS states in an N=2 supersymmetric 4d gauge theory coupled to a supersymmetric surface defect. When the theory and defect are compactified on a circle, we get a 3d theory with a supersymmetric line operator, corresponding to a hyperholomorphic connection on a vector bundle over a hyperkahler space. The 2d-4d wall-crossing formula can be interpreted as a smoothness condition for this hyperholomorphic connection. We explain how the 2d-4d BPS spectrum can be determined for 4d theories of class S, that is, for those theories obtained by compactifying the six-dimensional (0,2) theory with a partial topological twist on a punctured Riemann surface C. For such theories there are canonical surface defects. We illustrate with several examples in the case of A_1 theories of class S. Finally, we indicate how our results can be used to produce solutions to the A_1 Hitchin equations on the Riemann surface C.Comment: 170 pages, 45 figure

Exact and Asymptotic Degeneracies of Small Black Holes

We examine the recently proposed relations between black hole entropy and the topological string in the context of type II/heterotic string dual models. We consider the degeneracies of perturbative heterotic BPS states. In several examples with N=4 and N=2 supersymmetry, we show that the macroscopic degeneracy of small black holes agrees to all orders with the microscopic degeneracy, but misses non-perturbative corrections which are computable on the heterotic side. Using these examples we refine the previous proposals and comment on their domain of validity as well as on the relevance of helicity supertraces.Comment: 35pp. harvmac b-mode; v2 is substantially rewritten and includes new results; v3 contains further clarifications, and some new results; v3: final version to match published versio

T-Duality, and the K-Theoretic Partition Function of TypeIIA Superstring Theory

We study the partition function of type IIA string theory on 10-manifolds of the form T^2 x X where X is 8-dimensional, compact, and spin. We pay particular attention to the effects of the topological phases in the supergravity action implied by the K-theoretic formulation of RR fields, and we use these to check the T-duality invariance of the partition function. We find that the partition function is only T-duality invariant when we take into account the T-duality anomalies in the RR sector, the fermionic path integral (including 4-fermi interaction terms), and 1-loop corrections including worldsheet instantons. We comment on applications of our computation to speculations about the role of the Romans mass in M-theory. We also discuss some issues which arise when one attempts to extend these considerations to checking the full U-duality invariance of the theory.Comment: 73 pages, harvmac, b-mod