Complete Nondiagonal Reflection Matrices of RSOS/SOS and Hard Hexagon Models

In this paper we compute the most general nondiagonal reflection matrices of the RSOS/SOS models and hard hexagon model using the boundary Yang-Baxter equations. We find new one-parameter family of reflection matrices for the RSOS model in addition to the previous result without any parameter. We also find three classes of reflection matrices for the SOS model, which has one or two parameters. For the hard hexagon model which can be mapped to RSOS(5) model by folding four RSOS heights into two, the solutions can be obtained similarly with a main difference in the boundary unitarity conditions. Due to this, the reflection matrices can have two free parameters. We show that these extra terms can be identified with the `decorated' solutions. We also generalize the hard hexagon model by `folding' the RSOS heights of the general RSOS(p) model and show that they satisfy the integrability conditions such as the Yang- Baxter and boundary Yang-Baxter equations. These models can be solved using the results for the RSOS models.Comment: 18pages,Late

On the boundary form factor program

Boundary form factor axioms are derived for the matrix elements of local boundary operators in integrable 1+1 dimensional boundary quantum field theories using the analyticity properties of correlators via the boundary reduction formula. Minimal solutions are determined for the integrable boundary perturbations of the free boson, free fermion (Ising), Lee-Yang and sinh-Gordon models and the two point functions calculated from them are checked against the exact solutions in the free cases and against the conformal data in the ultraviolet limit for the Lee-Yang model. In the case of the free boson/fermion the dimension of the solution space of the boundary form factor equation is shown to match the number of independent local operators. We obtain excellent agreement which proves not only the correctness of the solutions but also confirms the form factor axioms.Comment: 38 pages, 17 eps figures, LaTeX, References adde

Form factors in the Bullough-Dodd related models: The Ising model in a magnetic field

We consider particular modification of the free-field representation of the form factors in the Bullough-Dodd model. The two-particles minimal form factors are excluded from the construction. As a consequence, we obtain convenient representation for the multi-particle form factors, establish recurrence relations between them and study their properties. The proposed construction is used to obtain the free-field representation of the lightest particles form factors in the $\Phi_{1,2}$ perturbed minimal models. As a significant example we consider the Ising model in a magnetic field. We check that the results obtained in the framework of the proposed free-field representation are in agreement with the corresponding results obtained by solving the bootstrap equations.Comment: 20 pages; v2: some misprints, textual inaccuracies and references corrected; some references and remarks adde

Form-factors of the sausage model obtained with bootstrap fusion from sine-Gordon theory

We continue the investigation of massive integrable models by means of the bootstrap fusion procedure, started in our previous work on O(3) nonlinear sigma model. Using the analogy with SU(2) Thirring model and the O(3) nonlinear sigma model we prove a similar relation between sine-Gordon theory and a one-parameter deformation of the O(3) sigma model, the sausage model. This allows us to write down a free field representation for the Zamolodchikov-Faddeev algebra of the sausage model and to construct an integral representation for the generating functions of form-factors in this theory. We also clear up the origin of the singularities in the bootstrap construction and the reason for the problem with the kinematical poles.Comment: 16 pages, revtex; references added, some typos corrected. Accepted for publication in Physical Review

Determining matrix elements and resonance widths from finite volume: the dangerous mu-terms

The standard numerical approach to determining matrix elements of local operators and width of resonances uses the finite volume dependence of energy levels and matrix elements. Finite size corrections that decay exponentially in the volume are usually neglected or taken into account using perturbation expansion in effective field theory. Using two-dimensional sine-Gordon field theory as "toy model" it is shown that some exponential finite size effects could be much larger than previously thought, potentially spoiling the determination of matrix elements in frameworks such as lattice QCD. The particular class of finite size corrections considered here are mu-terms arising from bound state poles in the scattering amplitudes. In sine-Gordon model, these can be explicitly evaluated and shown to explain the observed discrepancies to high precision. It is argued that the effects observed are not special to the two-dimensional setting, but rather depend on general field theoretic features that are common with models relevant for particle physics. It is important to understand these finite size corrections as they present a potentially dangerous source of systematic errors for the determination of matrix elements and resonance widths.Comment: 26 pages, 13 eps figures, LaTeX2e fil

Exact S-matrices for supersymmetric sigma models and the Potts model

We study the algebraic formulation of exact factorizable S-matrices for integrable two-dimensional field theories. We show that different formulations of the S-matrices for the Potts field theory are essentially equivalent, in the sense that they can be expressed in the same way as elements of the Temperley-Lieb algebra, in various representations. This enables us to construct the S-matrices for certain nonlinear sigma models that are invariant under the Lie ``supersymmetry'' algebras sl(m+n|n) (m=1,2; n>0), both for the bulk and for the boundary, simply by using another representation of the same algebra. These S-matrices represent the perturbation of the conformal theory at theta=pi by a small change in the topological angle theta. The m=1, n=1 theory has applications to the spin quantum Hall transition in disordered fermion systems. We also find S-matrices describing the flow from weak to strong coupling, both for theta=0 and theta=pi, in certain other supersymmetric sigma models.Comment: 32 pages, 8 figure

Ranging behaviour of translocated roe deer in a Mediterranean habitat: seasonal and altitudinal influences on home range size and patterns of range use

In this study we investigated the causes of seasonal variation in the home ranges of roe deer reintroduced to the Gardunha Mountains (Portugal). From May 2002 to April 2003, 1 year after the animals had been released, we collected data using radio-tracking techniques for five monitored animals (two males and three females). We found differences in the size of home ranges between seasons, with home ranges larger in summer than winter (minimum convex polygon peeled to 95%: summer 409.64 +/- 98.20 ha, winter 116.20 +/- 17.90 ha). This is contrary to evidence from central and northern Europe, where home ranges are typically larger in winter than summer. Moreover, two of the sampled females and one of the males tended to use higher elevations in summer. Comparisons between Mediterranean populations and those in central and northern Europe showed that Mediterranean populations in the winter easily fulfil their needs within a small area, whereas in the hot dry summer a larger area is needed. Furthermore, individuals prefer a higher, cooler mountainous habitat in summer, which is likely to be a means of avoiding warmer temperatures

Modeling the innate inflammatory cGAS/STING pathway: sexually dimorphic effects on microglia and cognition in obesity and prediabetes

IntroductionThe prevalence of obesity, prediabetes, and diabetes continues to grow worldwide. These metabolic dysfunctions predispose individuals to neurodegenerative diseases and cognitive impairment, including dementias such as Alzheimer’s disease and Alzheimer’s disease related dementias (AD/ADRD). The innate inflammatory cGAS/STING pathway plays a pivotal role in metabolic dysfunction and is an emerging target of interest in multiple neurodegenerative diseases, including AD/ADRD. Therefore, our goal was to establish a murine model to specifically target the cGAS/STING pathway to study obesity- and prediabetes-induced cognitive impairment.MethodsWe performed two pilot studies in cGAS knockout (cGAS-/-) male and female mice designed to characterize basic metabolic and inflammatory phenotypes and examine the impact of high-fat diet (HFD) on metabolic, inflammatory, and cognitive parameters.ResultscGAS-/- mice displayed normal metabolic profiles and retained the ability to respond to inflammatory stimuli, as indicated by an increase in plasma inflammatory cytokine production in response to lipopolysaccharide injection. HFD feeding caused expected increases in body weight and decreases in glucose tolerance, although onset was accelerated in females versus males. While HFD did not increase plasma or hippocampal inflammatory cytokine production, it did alter microglial morphology to a state indicative of activation, particularly in female cGAS-/- mice. However, HFD negatively impacted cognitive outcomes in male, but not female animals.DiscussionCollectively, these results suggest that cGAS-/- mice display sexually dimorphic responses to HFD, possibly based on differences in microglial morphology and cognition