The Congruence Subgroup Theorem and Units of Symmetric Group Rings

We work an example that illustrate the strong connection between K-Theory and Group Rings

Quantizing String Theory in AdS_5 X S^5: Beyond the pp-Wave

In a certain kinematic limit, where the effects of spacetime curvature (and other background fields) greatly simplify, the light-cone gauge world-sheet action for a type IIB superstring on AdS_5 x S^5 reduces to that of a free field theory. It has been conjectured by Berenstein, Maldacena, and Nastase that the energy spectrum of this string theory matches the dimensions of operators in the appropriately defined large R-charge large-N_c sector of N=4 supersymmetric Yang--Mills theory in four dimensions. This holographic equivalence is thought to be exact, independent of any simplifying kinematic limits. As a step toward verifying this larger conjecture, we have computed the complete set of first curvature corrections to the spectrum of light-cone gauge string theory that arises in the expansion of AdS_5 x S^5 about the plane-wave limit. The resulting spectrum has the complete dependence on lambda = g_YM^2 N_c; corresponding results in the gauge theory are known only to second order in lambda. We find precise agreement to this order, including the N=4 extended supermultiplet structure. In the process, we demonstrate that the complicated schemes put forward in recent years for defining the Green--Schwarz superstring action in background Ramond-Ramond fields can be reduced to a practical (and correct) method for quantizing the string.Comment: 39 pages; substantial improvement

Parental Influence Factors Affecting Christian Faith Maturity of Children through Adolescence

The role that parents play in the faith formation of their children is and has been historically significant. Modeling their religious beliefs as well as verbalizing them play an important part in the child\u27s view of God. It has also been found as this paper will articulate, that participation in the church life of the congregation and service projects are also an integral part of the development of the child\u27s faith development into the adolescent years. This paper will review the importance of the parents as the primary participants of their own child\u27s faith destiny and give applicable results for church leaders based from the findings of the research given

Giant graviton oscillators

A Dissertation submitted to the Faculty of Science, University of the Witwatersrand, in fulfilment of the requirements for the degree of Master of Science. 14 May 2013We study the action of the dilatation operator on restricted Schur polynomials labeled by Young diagrams with p long columns or p long rows. A new version of Schur-Weyl duality provides a powerful approach to the computation and manipulation of the symmetric group operators appearing in the restricted Schur polynomials. Using this new technology, we are able to evaluate the action of the one loop dilatation operator. The result has a direct and natural connection to the Gauss Law constraint for branes with a compact world volume. Generalzing previous results, we find considerable evidence that the dilatation operator reduces to a decoupled set of harmonic oscillators. This strongly suggests that integrability in N = 4 super Yang-Mills theory is not just a feature of the planar limit, but extends to other large N but non-planar limits

The Atrahasis Epic and its place in Babylonian literature.

The purpose of this study is to present, for the first time, the Epic of Atrahasis, as far as extant, in transliteration and translation (chapters II, III), and to examine it beside other Babylonian compositions containing similar material. Until 1965 only some three hundred lines of the Epic were known. That year saw the publication of the cuneiform text of some late Assyrian fragments by W.G. Lambert, and of two large Old Babylonian tablets by the writer (Cuneiform Texts XLVI). This new material, together with some unpublished texts, brings the number of lines represented to nearly one thousand (chapter 1) The large number of manuscripts of the work attest its popularity and importance. When the narrative of the creation of man is compared with other Mesopotamian texts, clear affinities are apparent with certain Sumerian and Akkadian traditions. Moreover, it can be shown that it probably formed a major source for the compilation of the later 'Babylonian Genesis', Enuma elish (chapter V). The second major theme, the Flood, is compared with other Flood Stories; parts of that narrative contained in the Gilgamesh Epic are identical with passages in the Atrahasis Epic, from which it is shown they were very probably borrowed (chapter VI). Certain sections within the poem reveal political institutions or practices of interest for the study of 'Primitive Democracy', of Babylonian concepts of remote history, and of traditions preserved in the King Lists (chapter VII). As a major literary work, the Epic of Atrahasis is shown to provide new material for investigation of the syntax and prosody of the 'Golden Age' of Akkadian literature (chapter IV). Obvious and important similarities to Hebrew tradition, closer in many points in Atrahasis than in any other Babylonian compositions, and the more remote comparisons with Greek legends fall beyond the scope of this investigation, but some indication of these is given (chapter VIII)