On the boundary Ising model with disorder operators

We extend the well-known method of calculating bulk correlation functions of the conformal Ising model via bosonisation to situations with boundaries. Oshikawa and Affleck have found the boundary states of two decoupled Ising models in terms of the orbifold of a single free boson compactified on a circle of radius r=1; we adapt their results to include disorder operators. Using these boundary states we calculate the expectation value of a single disorder field on a cylinder with free boundary conditions and show that in the appropriate limits we recover the standard and frustrated partition functions. We also show how to calculate Ising correlation functions on the upper half plane.Comment: 12 pages, Latex2e, 6 figure

'I'm learning nature now with them': what can a holistic perspective contribute to our understanding of the influential relations between young children, adults and a natural environment?

There is a contemporary concern about children’s loss of contact with the natural world and its associated benefits. Children’s reduced independent mobility is an influential factor and there is growing recognition of an interdependence between child and adult in accessing outdoor play. This research explores a gap in literature through considering impacts on adults in sharing outdoor experiences with children. A Froebelian holistic perspective has been foregrounded within this due to its understanding of child, adult and natural environment relations according to their mutual benefit. This has been investigated though a suburban preschool’s organization of family trips to local natural environments. Twelve participant families with children between two and four years old have formed the focus of research activity. A sensory ethnography approach has framed use of child-worn Go-Pros™ on trips and this footage has formed the basis for sensory elicitation interviews with adults. Fifteen hours of Go-Pro™ footage have been reviewed along with eleven hours of audio-recorded parent reflections. Analysis of these materials has drawn upon a vocabulary of holistic relations offered by the theory of the evolution of human consciousness (Gebser, 1949). This vocabulary gives equal value to the relational qualities expressed by adult and child (Chawla, 2002) and offers a lens through which to consider Froebelian pedagogical relationships. Findings have highlighted the potential for children to draw adults into immersive sensory experiences, big questions, and storied relations with their immediate surroundings. This can balance an adult potential to draw children towards a capacity for abstract relations with a whole or global context. Each can be considered significant in forming rich, thick, continuous connections between individual and whole and can align with sustainability thinking in a need to act local but think global. Froebelian philosophy may now offer a source of guidance towards an education for sustainable development through a path of familiar early years practices revitalized by a holistic logic

A non-rational CFT with c=1 as a limit of minimal models

We investigate the limit of minimal model conformal field theories where the central charge approaches one. We conjecture that this limit is described by a non-rational CFT of central charge one. The limiting theory is different from the free boson but bears some resemblance to Liouville theory. Explicit expressions for the three point functions of bulk fields are presented, as well as a set of conformal boundary states. We provide analytic and numerical arguments in support of the claim that this data forms a consistent CFT.Comment: latex2e, 37 pages, 4 figure

The SBI Program and Student Outcomes: A Study of Business Policy Classes

This study represents a preliminary inquiry ID to determine the value of combining SBI and Policy into a singular curriculum. A comparison of this combined formal was made wi1h the traditional Policy course. A slightly modified Job Diagnostic Survey (Hackman & Oldham, 1975) and a skills/usefulness scale (Hoffman, Fon1eno1 & Viswanathan, 1990) was administered to assess the difference between the two groups. Results suggested that the combined format met or exceeded the ou1comes of the traditional Policy course

Defects in the Tri-critical Ising model

We consider two different conformal field theories with central charge c=7/10. One is the diagonal invariant minimal model in which all fields have integer spins; the other is the local fermionic theory with superconformal symmetry in which fields can have half-integer spin. We construct new conformal (but not topological or factorised) defects in the minimal model. We do this by first constructing defects in the fermionic model as boundary conditions in a fermionic theory of central charge c=7/5, using the folding trick as first proposed by Gang and Yamaguchi. We then acting on these with interface defects to find the new conformal defects. As part of the construction, we find the topological defects in the fermionic theory and the interfaces between the fermionic theory and the minimal model. We also consider the simpler case of defects in the theory of a single free fermion and interface defects between the Ising model and a single fermion as a prelude to calculations in the tri-critical Ising model.Comment: 54 pages, 5 figures, version as accepted for publication with minor change

The reflection coefficient for minimal model conformal defects from perturbation theory

We consider a class of conformal defects in Virasoro minimal models that have been defined as fixed points of the renormalisation group and calculate the leading contribution to the reflection coefficient for these defects. This requires several structure constants of the operator algebra of the defect fields, for which we present a derivation in detail. We compare our results with our recent work on conformal defects in the tricritical Ising model.Comment: 22 pages; v2: minor changes, defect field transformation law clarified, reference adde

Characters of the W3 algebra

Traces of powers of the zero mode in the W3 Algebra have recently been found to be of interest, for example in relation to Black Hole thermodynamics, and arise as the terms in an expansion of the full characters of the algebra. We calculate the first few such powers in two cases. Firstly, we find the traces in the 3-state Potts model by using null vectors to derive modular differential equations for the traces. Secondly, we calculate the exact results for Verma module representations. We compare our two methods with each other and the result of brute-force diagonalisation for low levels and find complete agreement.Comment: v2: Numerous small changes, version to appear in JHEP, 22 pages. v3: Typos corrected, matches published version, 22 page

A pitfall of piecewise-polytropic equation of state inference

The only messenger radiation in the Universe which one can use to statistically probe the Equation of State (EOS) of cold dense matter is that originating from the near-field vicinities of compact stars. Constraining gravitational masses and equatorial radii of rotating compact stars is a major goal for current and future telescope missions, with a primary purpose of constraining the EOS. From a Bayesian perspective it is necessary to carefully discuss prior definition; in this context a complicating issue is that in practice there exist pathologies in the general relativistic mapping between spaces of local (interior source matter) and global (exterior spacetime) parameters. In a companion paper, these issues were raised on a theoretical basis. In this study we reproduce a probability transformation procedure from the literature in order to map a joint posterior distribution of Schwarzschild gravitational masses and radii into a joint posterior distribution of EOS parameters. We demonstrate computationally that EOS parameter inferences are sensitive to the choice to define a prior on a joint space of these masses and radii, instead of on a joint space interior source matter parameters. We focus on the piecewise-polytropic EOS model, which is currently standard in the field of astrophysical dense matter study. We discuss the implications of this issue for the field.Comment: 16 pages, 9 figures. Accepted for publication in MNRA

Reflection and Transmission for Conformal Defects

We consider conformal defects joining two conformal field theories along a line. We define two new quantities associated to such defects in terms of expectation values of the stress tensors and we propose them as measures of the reflectivity and transmissivity of the defect. Their properties are investigated and they are computed in a number of examples. We obtain a complete answer for all defects in the Ising model and between certain pairs of minimal models. In the case of two conformal field theories with an enhanced symmetry we restrict ourselves to non-trivial defects that can be obtained by a coset construction.Comment: 32 pages + 13 pages appendix, 12 figures; v2: added eqns (2.7), (2.8) and refs [6,7,39,40], version published in JHE