Ising Field Theory on a Pseudosphere

We show how the symmetries of the Ising field theory on a pseudosphere can be exploited to derive the form factors of the spin fields as well as the non-linear differential equations satisfied by the corresponding two-point correlation functions. The latter are studied in detail and, in particular, we present a solution to the so-called connection problem relating two of the singular points of the associated Painleve VI equation. A brief discussion of the thermodynamic properties is also presented.Comment: 39 pages, 6 eps figures, uses harvma

Form factors of twist fields in the lattice Dirac theory

We study U(1) twist fields in a two-dimensional lattice theory of massive Dirac fermions. Factorized formulas for finite-lattice form factors of these fields are derived using elliptic parametrization of the spectral curve of the model, elliptic determinant identities and theta functional interpolation. We also investigate the thermodynamic and the infinite-volume scaling limit, where the corresponding expressions reduce to form factors of the exponential fields of the sine-Gordon model at the free-fermion point.Comment: 20 pages, 2 figure

Evolution of Genes Neighborhood Within Reconciled Phylogenies: An Ensemble Approach

Context The reconstruction of evolutionary scenarios for whole genomes in terms of genome rearrangements is a fundamental problem in evolutionary and comparative genomics. The DeCo algorithm, recently introduced by Bérard et al., computes parsimonious evolutionary scenarios for gene adjacencies, from pairs of reconciled gene trees. However, as for many combinatorial optimization algorithms, there can exist many co-optimal, or slightly sub-optimal, evolutionary scenarios that deserve to be considered. Contribution We extend the DeCo algorithm to sample evolutionary scenarios from the whole solution space under the Boltzmann distribution, and also to compute Boltzmann probabilities for specific ancestral adjacencies. Results We apply our algorithms to a dataset of mammalian gene trees and adjacencies, and observe a significant reduction of the number of syntenic conflicts observed in the resulting ancestral gene adjacencies

Finite Temperature Dynamical Correlations in Massive Integrable Quantum Field Theories

We consider the finite-temperature frequency and momentum dependent two-point functions of local operators in integrable quantum field theories. We focus on the case where the zero temperature correlation function is dominated by a delta-function line arising from the coherent propagation of single particle modes. Our specific examples are the two-point function of spin fields in the disordered phase of the quantum Ising and the O(3) nonlinear sigma models. We employ a Lehmann representation in terms of the known exact zero-temperature form factors to carry out a low-temperature expansion of two-point functions. We present two different but equivalent methods of regularizing the divergences present in the Lehmann expansion: one directly regulates the integral expressions of the squares of matrix elements in the infinite volume whereas the other operates through subtracting divergences in a large, finite volume. Our central results are that the temperature broadening of the line shape exhibits a pronounced asymmetry and a shift of the maximum upwards in energy ("temperature dependent gap"). The field theory results presented here describe the scaling limits of the dynamical structure factor in the quantum Ising and integer spin Heisenberg chains. We discuss the relevance of our results for the analysis of inelastic neutron scattering experiments on gapped spin chain systems such as CsNiCl3 and YBaNiO5.Comment: 54 pages, 10 figure

Calogero-Sutherland eigenfunctions with mixed boundary conditions and conformal field theory correlators

We construct certain eigenfunctions of the Calogero-Sutherland hamiltonian for particles on a circle, with mixed boundary conditions. That is, the behavior of the eigenfunction, as neighbouring particles collide, depend on the pair of colliding particles. This behavior is generically a linear combination of two types of power laws, depending on the statistics of the particles involved. For fixed ratio of each type at each pair of neighboring particles, there is an eigenfunction, the ground state, with lowest energy, and there is a discrete set of eigenstates and eigenvalues, the excited states and the energies above this ground state. We find the ground state and special excited states along with their energies in a certain class of mixed boundary conditions, interpreted as having pairs of neighboring bosons and other particles being fermions. These particular eigenfunctions are characterised by the fact that they are in direct correspondence with correlation functions in boundary conformal field theory. We expect that they have applications to measures on certain configurations of curves in the statistical O(n) loop model. The derivation, although completely independent from results of conformal field theory, uses ideas from the "Coulomb gas" formulation.Comment: 35 pages, 9 figure

Calculus on manifolds of conformal maps and CFT

In conformal field theory (CFT) on simply connected domains of the Riemann sphere, the natural conformal symmetries under self-maps are extended, in a certain way, to local symmetries under general conformal maps, and this is at the basis of the powerful techniques of CFT. Conformal maps of simply connected domains naturally have the structure of an infinite-dimensional groupoid, which generalizes the finite-dimensional group of self-maps. We put a topological structure on the space of conformal maps on simply connected domains, which makes it into a topological groupoid. Further, we (almost) extend this to a local manifold structure based on the infinite-dimensional Frechet topological vector space of holomorphic functions on a given domain A. From this, we develop the notion of conformal A-differentiability at the identity. Our main conclusion is that quadratic differentials characterizing cotangent elements on the local manifold enjoy properties similar to those of the holomorphic stress-energy tensor of CFT; these properties underpin the local symmetries of CFT. Applying the general formalism to CFT correlation functions, we show that the stress-energy tensor is exactly such a quadratic differential. This is at the basis of constructing the stress-energy tensor in conformal loop ensembles. It also clarifies the relation between Cardy's boundary conditions for CFT on simply connected domains, and the expression of the stress-energy tensor in terms of metric variations.Comment: v1: 51 pages, 5 figures. v2: 56 pages, corrections and clarifications. v3: 53 pages, one substantial addition (groupoid structure), discussion further clarified and simplified. v4: 59 pages, introduction improved, with a discussion on the relations with previous works. Published versio

The VAST Survey - III. The multiplicity of A-type stars within 75 pc

With a combination of adaptive optics imaging and a multi-epoch common proper motion search, we have conducted a large volume-limited (D $\le$ 75 pc) multiplicity survey of A-type stars, sensitive to companions beyond 30 au. The sample for the Volume-limited A-STar (VAST) survey consists of 435 A-type stars: 363 stars were observed with adaptive optics, 228 stars were searched for wide common proper motion companions and 156 stars were measured with both techniques. The projected separation coverage of the VAST survey extends from 30 to 45,000 au. A total of 137 stellar companions were resolved, including 64 new detections from the VAST survey, and the companion star fraction, projected separation distribution and mass ratio distribution were measured. The separation distribution forms a log-normal distribution similar to the solar-type binary distribution, but with a peak shifted to a significantly wider value of 387 (+132,-98) au. Integrating the fit to the distribution over the 30 to 10,000 au observed range, the companion star fraction for A-type stars is estimated as 33.8%+-2.6%. The mass ratio distribution of closer (<125 au) binaries is distinct from that of wider systems, with a flat distribution for close systems and a distribution that tends towards smaller mass ratios for wider binaries. Combining this result with previous spectroscopic surveys of A-type stars gives an estimate of the total companion star fraction of 68.9%+-7.0%. The most complete assessment of higher order multiples was estimated from the 156-star subset of the VAST sample with both adaptive optics and common proper motion measurements, combined with a literature search for companions, yielding a lower limit on the frequency of single, binary, triple, quadruple and quintuple A-type star systems of 56.4 (-4.0,+3.8), 32.1 (-3.5,+3.9), 9.0 (-1.8,+2.8), 1.9 (-0.6,+1.8) and 0.6 (-0.2,+1.4) per cent, respectively.Comment: 46 pages, 24 figures. Accepted for publication in the Monthly Notices of the Royal Astronomical Society, 7th October 201