Periodic Arrays of M2-Branes

We consider periodic arrays of M2-branes in the ABJM model in the spirit of a circle compactification to D2-branes in type IIA string theory. The result is a curious formulation of three-dimensional maximally supersymmetric Yang-Mills theory in terms of fermions, seven transverse scalars, a non-dynamical gauge field and an additional scalar `dual gluon'. Upon further T-duality on a transverse torus we obtain a non-manifest-Lorentz-invariant description of five-dimensional maximally supersymmetric Yang-Mills. Here the additional scalar field can be thought of as the components of a two-form along the torus. This action can be viewed as an M-theory description of M5-branes on ${\mathbb T}^3$.Comment: 20 pages, 1 figure, v3: typos corrected, published versio

The holographic supersymmetric Renyi entropy in five dimensions

We compute the supersymmetric Renyi entropy across an entangling three-sphere for five-dimensional superconformal field theories using localization. For a class of USp(2N) gauge theories we construct a holographic dual 1/2 BPS black hole solution of Euclidean Romans F(4) supergravity. The large N limit of the gauge theory results agree perfectly with the supergravity computations.Comment: 19 page

Multiple M-branes and 3-algebras

The purpose of this thesis is to explore the properties of multiple coincident M2- and M5-branes. We begin with a review of the BLG and ABJM models of multiple M2-branes and our focus will be on their formulation in terms of 3-algebras. We then examine the coupling of multiple M2-branes to the background 3-form and 6-form gauge fields of eleven-dimensional supergravity. In particular we show in detail how a natural generalisation of the Myers flux-terms, along with the resulting curvature of the background metric, leads to mass terms in the effective field theory. Working to lowest nontrivial order in fermions, we demonstrate the supersymmetric invariance of the four-derivative order corrected Lagrangian of the Euclidean BLG theory and determine the theory's higher derivative corrected supersymmetry transformations. The supersymmetry algebra is also shown to close on the scalar and gauge fields. We also consider periodic arrays of M2-branes in the ABJM model in the spirit of a circle compactification to D2-branes in type IIA string theory. The result is a curious formulation of three-dimensional maximally supersymmetric Yang-Mills theory. Upon further T-duality on a transverse torus we obtain a non-manifest-Lorentz-invariant description of five-dimensional maximally supersymmetric Yang-Mills which can be viewed as an M-theory description of M5-branes on $\mathbb{T}^3$. After reviewing work to describe multiple M5-branes using 3-algebras we show how the resulting novel system of equations reduces to one-dimensional motion on instanton moduli space. Quantisation leads to the previous light-cone proposal of the (2,0) theory, generalised to include a potential that arises on the Coulomb branch as well as couplings to background gauge and self-dual 2-form fields.Comment: PhD Thesis, 155 pages, 1 figur

Macrocyclic compounds derived from Perfluoro-4-isopropylpyridine

PerflLioro-4-isopropylpyridine (1) has been shown to undergo nucleophilic substitution reactions with wide range of nucleophiles and was thus demonstrated to behave as a powerful regioselective electrophile in most cases.(INSERT DIAGRAM) This work has enabled a series of highly fluorinated macrocyclic compounds to be synthesised based on highly fluorinated pyridine derivatives.(INSERT DIAGRAM) Polyfluoroalkylation and nucleophilic substitution in tetrafluoropyrimidine and tetrafluorophthalonitrile give highly fluorinated products that react readily with nucleophiles.(INSERT DIAGRAM

Localization on Three-Manifolds

We consider supersymmetric gauge theories on Riemannian three-manifolds with the topology of a three-sphere. The three-manifold is always equipped with an almost contact structure and an associated Reeb vector field. We show that the partition function depends only on this vector field, giving an explicit expression in terms of the double sine function. In the large N limit our formula agrees with a recently discovered two-parameter family of dual supergravity solutions. We also explain how our results may be applied to prove vortex-antivortex factorization. Finally, we comment on the extension of our results to three-manifolds with non-trivial fundamental group.Comment: 34 pages; v2: discussion of vortex factorization added; v3: minor correction

Fast-growth companies in Scotland

Research shows that fast - growth companies contribute disproportionately to jobs growth, and, compared to non - fast growth companies, tend to be more innovative, and are more likely to be exporters 2 . Therefore, developing a better understanding of fast - growth companies in Scotland will contribute to our evidence - base on their contribution to productivity performance. This paper presents new evidence on fast - growth companies in Scotland. For this analysis, we have considered companies in the turnover sizeband of between £5m and £25m, and that have a minimum of 10 employees. Fast - growth companies are defined as those within this sizeband that achieved turnover growth of at least 60% between 2011 and 2014

Supersymmetric solutions to Euclidean Romans supergravity

We study Euclidean Romans supergravity in six dimensions with a non-trivial Abelian R-symmetry gauge field. We show that supersymmetric solutions are in one-to-one correspondence with solutions to a set of differential constraints on an SU(2) structure. As an application of our results we (i) show that this structure reduces at a conformal boundary to the five-dimensional rigid supersymmetric geometry previously studied by the authors, (ii) find a general expression for the holographic dual of the VEV of a BPS Wilson loop, matching an exact field theory computation, (iii) construct holographic duals to squashed Sasaki-Einstein backgrounds, again matching to a field theory computation, and (iv) find new analytic solutions.Comment: 31 pages; v2: published version (with reference added

Two-dimensional analysis of natural convection and radiation in utilidors

Thesis (Ph.D.) University of Alaska Fairbanks, 1997Central heating plants are often used on large building complexes such as university campuses or military bases. Utilidors can be used to contain heat distribution lines and other utilities between a utility station and serviced buildings. Traditional thermal analysis of utilidors is one-dimensional, with heat transfer correlations used to estimate the effects of convection, radiation, and two-dimensional geometric effects. The expanding capabilities of computers and numerical methods suggest that more detailed analysis and possibly more energy-efficient designs could be obtained. This work examines current methods of estimating the convection and radiation that occur across an air space in square and rectangular enclosures and compares them with numerical and experimental data. A numerical model was developed that solves the energy, momentum, and continuity equations for the primitive variables in two dimensions; radiation between free surfaces was also included. Physical experiments were conducted with two 10-ft-long apparatuses; one had a 1-ft $\times$ 1-ft cross section, the other was 2 ft $\times$ 4 ft. Several pipe sizes and configurations were studied with the 1-ft $\times$ 1-ft apparatus. The 2-ft $\times$ 4-ft apparatus was limited to containing 4- and 8-inch insulated pipes. Corresponding numerical studies were conducted. Difficulties in modeling large enclosures or those with large temperature differences (Rayleigh numbers above 10\sp7) were encountered. Results showed good agreement between numerical and experimental average heat transfer rates, and for insulated pipe cases these results also compared well with rates obtained from one-dimensional analysis. A new effective conductivity correlation for air in a square enclosure was developed, and its use was demonstrated in numerical conduction solutions and compared with full numerical convection and radiation solutions and with experimental data. Reasonably good results were achieved when there was a small temperature difference across the air gap