q-Deformation of the AdS5 x S5 Superstring S-matrix and its Relativistic Limit

A set of four factorizable non-relativistic S-matrices for a multiplet of fundamental particles are defined based on the R-matrix of the quantum group deformation of the centrally extended superalgebra su(2|2). The S-matrices are a function of two independent couplings g and q=exp(i\pi/k). The main result is to find the scalar factor, or dressing phase, which ensures that the unitarity and crossing equations are satisfied. For generic (g,k), the S-matrices are branched functions on a product of rapidity tori. In the limit k->infinity, one of them is identified with the S-matrix describing the magnon excitations on the string world sheet in AdS5 x S5, while another is the mirror S-matrix that is needed for the TBA. In the g->infinity limit, the rapidity torus degenerates, the branch points disappear and the S-matrices become meromorphic functions, as required by relativistic S-matrix theory. However, it is only the mirror S-matrix which satisfies the correct relativistic crossing equation. The mirror S-matrix in the relativistic limit is then closely related to that of the semi-symmetric space sine-Gordon theory obtained from the string theory by the Pohlmeyer reduction, but has anti-symmetric rather than symmetric bound states. The interpolating S-matrix realizes at the quantum level the fact that at the classical level the two theories correspond to different limits of a one-parameter family of symplectic structures of the same integrable system.Comment: 41 pages, late

On partial order semantics for SAT/SMT-based symbolic encodings of weak memory concurrency

Concurrent systems are notoriously difficult to analyze, and technological advances such as weak memory architectures greatly compound this problem. This has renewed interest in partial order semantics as a theoretical foundation for formal verification techniques. Among these, symbolic techniques have been shown to be particularly effective at finding concurrency-related bugs because they can leverage highly optimized decision procedures such as SAT/SMT solvers. This paper gives new fundamental results on partial order semantics for SAT/SMT-based symbolic encodings of weak memory concurrency. In particular, we give the theoretical basis for a decision procedure that can handle a fragment of concurrent programs endowed with least fixed point operators. In addition, we show that a certain partial order semantics of relaxed sequential consistency is equivalent to the conjunction of three extensively studied weak memory axioms by Alglave et al. An important consequence of this equivalence is an asymptotically smaller symbolic encoding for bounded model checking which has only a quadratic number of partial order constraints compared to the state-of-the-art cubic-size encoding.Comment: 15 pages, 3 figure

Infrared Helium-Hydrogen Line Ratios as a Measure of Stellar Effective Temperature

We have observed a large sample of compact planetary nebulae in the near-infrared to determine how the 2^1P-2^1S HeI line at 2.058um varies as a function of stellar effective temperature, Teff. The ratio of this line with HI Br g at 2.166um has often been used as a measure of the highest Teff present in a stellar cluster, and hence on whether there is a cut-off in the stellar initial mass function at high masses. However, recent photoionisation modelling has revealed that the behaviour of this line is more complex than previously anticipated. Our work shows that in most aspects the photoionisation models are correct. In particular, we confirm the weakening of the 2^1P-2^1S as Teff increases beyond 40000K. However, in many cases the model underpredicts the observed ratio when we consider the detailed physical conditions in the individual planetary nebulae. Furthermore, there is evidence that there is still significant 2^1P-2^1S HeI line emission even in the planetary nebulae with very hot (Teff>100000K) central stars. It is clear from our work that this ratio cannot be considered as a reliable measure of effective temperature on its own.Comment: 24 pages 11 figures (in 62 separate postscript files) Accepted for publication in Monthly Notices of the Royal Astronomical Societ

Near Infrared Spectra of Compact Planetary Nebulae

This paper continues our study of the behaviour of near infrared helium recombination lines in planetary nebula. We find that the 1.7007um 4^3D-3^3P HeI line is a good measure of the HeI recombination rate, since it varies smoothly with the effective temperature of the central star. We were unable to reproduce the observed data using detailed photoionisation models at both low and high effective temperatures, but plausible explanations for the difference exist for both. We therefore conclude that this line could be used as an indicator of the effective temperature in obscured nebula. We also characterised the nature of the molecular hydrogen emission present in a smaller subset of our sample. The results are consistent with previous data indicating that ultraviolet excitation rather than shocks is the main cause of the molecular hydrogen emission in planetary nebulae.Comment: Accepted for publication in MNRA

The Balby Seekers and Richard Farnworth

This paper describes the group of Seekers which flourished briefly in 1650 and 1651 around Balby, Warmsworth and Tickhill in South Yorkshire, and explores their origins. They may have numbered up to thirty, and had developed as radical puritans independently of any immediate local Separatist tradition or Grindletonian influence. They joined with George Fox on his arrival around December 1651, providing several pioneers who helped in launching the Quaker movement. These included Richard Farnworth, Thomas Aldam, Benjamin Nicholson, and John, Thomas and Margaret Killam, with Thomas and Elizabeth Stacy from Ballifield near Sheffield. Evidence is presented that Farnworth was born on 14th October 1627, and that he may have first encountered George Fox at Derby in early 1650

Bound States of the q-Deformed AdS5 x S5 Superstring S-matrix

The investigation of the q deformation of the S-matrix for excitations on the string world sheet in AdS5 x S5 is continued. We argue that due to the lack of Lorentz invariance the situation is more subtle than in a relativistic theory in that the nature of bound states depends on their momentum. At low enough momentum |p|<E the bound states transform in the anti-symmetric representation of the super-algebra symmetry and become the solitons of the Pohlmeyer reduced theory in the relativistic limit. At a critical momentum |p|=E they become marginally unstable, and at higher momenta the stable bound states are in the symmetric representation and become the familiar magnons in the string limit as q->1. This subtlety fixes a problem involving the consistency of crossing symmetry with the relativistic limit found in earlier work. With mirror kinematics, obtained after a double Wick rotation, the bound state structure is simpler and there are no marginally unstable bound states.Comment: 25 page