Conformal Field Theories, Representations and Lattice Constructions

An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory. This general approach is illustrated by considering the untwisted and $Z_2$-twisted theories, $H(\Lambda)$ and $\tilde H(\Lambda)$ respectively, which may be constructed from a suitable even Euclidean lattice $\Lambda$. Similarly, one may construct lattices $\Lambda_C$ and $\tilde\Lambda_C$ by analogous constructions from a doubly-even binary code $C$. In the case when $C$ is self-dual, the corresponding lattices are also. Similarly, $H(\Lambda)$ and $\tilde H(\Lambda)$ are self-dual if and only if $\Lambda$ is. We show that $H(\Lambda_C)$ has a natural ``triality'' structure, which induces an isomorphism $H(\tilde\Lambda_C)\equiv\tilde H(\Lambda_C)$ and also a triality structure on $\tilde H(\tilde\Lambda_C)$. For $C$ the Golay code, $\tilde\Lambda_C$ is the Leech lattice, and the triality on $\tilde H(\tilde\Lambda_C)$ is the symmetry which extends the natural action of (an extension of) Conway's group on this theory to the Monster, so setting triality and Frenkel, Lepowsky and Meurman's construction of the natural Monster module in a more general context. The results also serve to shed some light on the classification of self-dual CFT's. We find that of the 48 theories $H(\Lambda)$ and $\tilde H(\Lambda)$ with central charge 24 that there are 39 distinct ones, and further that all 9 coincidences are accounted for by the isomorphism detailed above, induced by the existence of a doubly-even self-dual binary code.Comment: 65 page

Shapes and Dynamics from the Time-Dependent Mean Field

Explaining observed properties in terms of underlying shape degrees of freedom is a well--established prism with which to understand atomic nuclei. Self--consistent mean--field models provide one tool to understand nuclear shapes, and their link to other nuclear properties and observables. We present examples of how the time--dependent extension of the mean--field approach can be used in particular to shed light on nuclear shape properties, particularly looking at the giant resonances built on deformed nuclear ground states, and at dynamics in highly-deformed fission isomers. Example calculations are shown of $^{28}$Si in the first case, and $^{240}$Pu in the latter case.Comment: 9 pages, 5 figures, to appear in proceedings of International Workshop "Shapes and Dynamics of Atomic Nuclei: Contemporary Aspects" (SDANCA-15), 8-10 October 2015, Sofia, Bulgari

Electromagnetic field application to underground power cable detection

Before commencing excavation or other work where power or other cables may be buried, it is important to determine the location of cables to ensure that they are not damaged. This paper describes a method of power-cable detection and location that uses measurements of the magnetic field produced by the currents in the cable, and presents the results of tests performed to evaluate the method. The cable detection and location program works by comparing the measured magnetic field signal with values predicted using a simple numerical model of the cable. Search coils are used as magnetic field sensors, and a measurement system is setup to measure the magnetic field of an underground power cable at a number of points above the ground so that it can detect the presence of an underground power cable and estimate its position. Experimental investigations were carried out using a model and under real site test conditions. The results show that the measurement system and cable location method give a reasonable prediction for the position of the target cable

Navajo texts

PM2009, ISO 639-3 : nav, Navajo language--Texts, Navajo Indians--Folklor

Non Abelian Sugawara Construction and the q-deformed N=2 Superconformal Algebra

The construction of a q-deformed N=2 superconformal algebra is proposed in terms of level 1 currents of ${\cal{U}}_{q} ({\widehat{su}}(2))$ quantum affine Lie algebra and a single real Fermi field. In particular, it suggests the expression for the q-deformed Energy-Momentum tensor in the Sugawara form. Its constituents generate two isomorphic quadratic algebraic structures. The generalization to ${\cal{U}}_{q} ({\widehat{su}}(N+1))$ is also proposed.Comment: AMSLATEX, 21page