Geometry of Topological Defects of Two-dimensional Sigma Models

A topological defect separating a pair of two-dimensional CFTs is a codimension one interface along which all components of the stress-energy tensor glue continuously. We study topological defects of the bosonic, (0,1)- and (0,2)-supersymmetric sigma models in two dimensions. We find a geometric classification of such defects closely analogous to that of A-branes of symplectic manifolds, with the role of symplectic form played instead by a neutral signature metric. Alternatively, we find a compact description in terms of a generalized metric on the product of the targets. In the (0,1) case, we describe the target space geometry of a bundle in which the fermions along the defect take values. In the (0,2) case, we describe the defects as being simultaneously A-branes and B-branes.Comment: 21 pages, late

Surface operators in four-dimensional topological gauge theory and Langlands duality

We study surface and line operators in the GL-twisted N=4 gauge theory in four dimensions. Their properties depend on the parameter t which determines the BRST operator of theory. For t=i we propose a complete description of the 2-category of surface operators in terms of module categories. We also determine the monoidal category of line operators which includes Wilson lines as special objects. For t=1 and t=0 we only discuss surface and line operators in the abelian case. Applications to the categorification of the local geometric Langlands duality and its quantum version are briefly described. In the appendices we discuss several 3d and 2d topological field theories with gauge fields. In particular, we explain a relationship between the category of branes in the gauged B-model and the equivariant derived category of coherent sheaves.Comment: 60 pages, 8 figure

Close-circuit domain quadruplets in BaTiO3_3 nanorods embedded in SrTiO3_3 film

Cylindrical BaTiO3 nanorods embedded in (100)-oriented SrTiO3 epitaxial film in a brush-like configuration are investigated in the framework of the Ginzburg-Landau-Devonshire model. It is shown that strain compatibility at BaTiO3/SrTiO3 interfaces keeps BaTiO3 nanorods in the rhombohedral phase even at room temperature. Depolarization field at the BaTiO3/SrTiO3 interfaces is reduced by an emission of the 109-degree or 71-degree domain boundaries. In case of nanorods of about 10-80 nm diameter, the ferroelectric domains are found to form a quadruplet with a robust flux-closure arrangement of the in-plane components of the spontaneous polarization. The out-of-plane components of the polarization are either balanced or oriented up or down along the nanorod axis. Switching of the out-of-plane polarization with coercive field of about $5.10^6$ V/m occurs as a collapse of a 71-degree cylindrical domain boundary formed at the curved circumference surface of the nanorod. The remnant domain quadruplet configuration is chiral, with the $C_4$ macroscopic symmetry. More complex stable domain configurations with coexisting clockwise and anticlockwise quadruplets contain interesting arrangement of strongly curved 71-degree boundaries.Comment: Erratta - corrected error in Fig.

N-body U and K matrix program

Computer program was devised to compute free-fall trajectories of satellites, allowing for injection errors and midcourse velocity perturbations. Program consists of trajectory perturbing program and N-body integrating conic program which can also be used as 2-body patch conic program

Future challenges of the impact agenda

This chapter acts as an afterword, summarising the main themes in the book, including the challenges presented by the UK impact agenda and how these challenges might look in the future

Research-led teaching in phonetics: an exercise in research literacy

Research-led teaching can take a number of different forms, including training students in research methods, exposing students to research, and engaging students in it as participants. This paper reports on an exercise to engage university students in phonetic research as part of a credit-bearing module by involving them in the research as participants and using an assessed reflective exercise to improve students’ understanding of aspects of phonetic research, i.e., research design and data collection. This enabled students to evaluate not only the research methodology, but also their roles as participants and as prospective researchers, thus improving their research literacy