A dissertation submitted to the faculty of science, University of the Witwatersrand, Johannesburg, in fulfillment of the requirements for the degree of Master of Science. July 6, 2017. / We study the collective field theory of a free multi-matrix model in the radial sector, which has an emergent 1/r2 term, and take the large N limit. We show that it is possible to generate 2−d metrics with generic dependence on the collective field Lagrange multiplier (μ) and potential and which are distinguished by the choice of the potential. The Lagrange multiplier is shown to depend on an induced scale parameter after an I.R. regularization and breaks scale invariance. The collective field sl(2, R) algebras of the free Hamiltonian and a related alternative compact operator only close in the absence of μ. We point out that the broken conformal symmetry is contained in the associated metrics which suggests that they are related to a Near-AdS2 geometry. We also comment on the resemblance of these metrics to black hole solutions. / MT2018

A thesis submitted to the Faculty of Science, University of the Witwatersrand, in fulfilment of the requirements for the degree of Doctor of Philosophy February 2017. / In this dissertation we exploit the Ads slash CFT correspondence to describe a system of strings suspended between giant gravitons. The strings can be in an excited state. The excitations of the strings can be given a particle-like description and are known as magnons. The proposed gauge invariant operators used to construct a complete description of this system belong to the su(2) sector of the N = 4 SYM. Using an open spin chain description of the suspended strings, the states of the system we consider enjoy an SU 2j2)2 symmetry. By making use of this symmetry, we compute the all loop anomalous dimensions of these operators. The spectrum of the dilatation operator in the su(2) sector of the theory is reproduced in the dual gravity description. In the dual theory, the energies of the magnons are computed using strings in a background LLM geometry and the results are in complete agreement with the anomalous dimensions of the operators we have considered. Using the symmetries enjoyed by our system we achieve a complete determination - up to an overall phase - of the reection/scattering matrix between a boundary magnon and a bulk magnon. Thus, although the open boundary conditions of the spin chain spoil integrability. The two-loop subleading correction to the dilatation operator is also explored. This subleading term corresponds to a correction of the magnon energies. The computation of this subleading term requires consideration of the giant's backreaction on their excitations. We nd that this backreaction implies a nontrivial mixing of the dual operators and this mixing is characterized completely. / MT2017

MSc., Faculty of Science, University of the Witwatersrand, 2011 / Anomalous dimensions are calculated for a certain class of operators in the restricted Schur polynomial basis in the large N limit. A new computationally simple form of the dilatation operator is derived and used in this dissertation. The class of operators investigated have bare dimension of O(N). Thus the calculation necessarily sums non-planar Feynmann diagrams as the planar approximation has broken down for operators of this size. The operators investigated have two long columns and the operators mix under the action of the dilatation operator, however the mixing of operators having a different number of columns is suppressed and can be neglected in the large N limit. The action of the one loop dilatation operator is explicitly calculated for the cases where the operators have two, three and four impurities and it is found that in a particular limit the action of the one loop dilatation operator reduces to that of a discrete second derivative. The lattice on which the discretised second derivative is defined is provided by the Young tableaux itself. The one loop dilatation operator is diagonalised numerically and produces a surprisingly simple linear spectrum, with interesting degeneracies. The spectrum can be understood in terms of a collection of harmonic oscillators. The frequencies of the oscillators are all multiples of 8g2Y M and can be related to the set of Young tableaux acted upon by the dilatation operator. This equivalence to harmonic oscillators generalises on previously found results in the BPS sector, and suggests that the system is integrable. The work presented here is based primarily on research carried out by R.de Mello Koch, V De Comarmond, and K. Jefferies in [1].

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Physics, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE / Vita. / Includes bibliographical references. / by Lawrence Maxwell Krauss. / Ph.D.

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A modern and straight forward summary of the necessary tools andconcepts needed to understand and work with gauge theory in a fibre bundle formalism. Due to the aim of being a quick but thorough introductionfull derivations are rarely included, but references to such are given wherethey have been omitted. General Relativity, although being a geometrical theory, in the sense that the gravitational force is described by the curvature of space-time, may not be derived from geometry like the other fundamental forces as in Yang-Mills theory. Thus, a possibility of unification lies in a geometrical derivation of gravity from gauge principles. By applying the presented formalism to the case of Gravity such a derivationis pursued along the lines of nonlinear realizations of the gauge group.

The motivation for this research was an improvement of the quality of the Earth’s gravity solutions from the GRACE mission data through an instrument-level study. The objective was a better understanding of the characteristics and sources of the highfrequency noise in the range of (0.02 ~ 0.1 Hz) in the dual one-way ranging (DOWR) and its effect on the gravity solution. For this purpose, the mathematical model of the DOWR observation was derived and the Allan variance was computed to establish an upper bound on the level of frequency instability of the ultra-stable oscillators (USO) to determine their contribution to the high-frequency noise. Because they are dominated by the high-frequency noise, the postfit residuals of the time derivative of the DOWR ranges were also examined to evaluate the contributions of various other factors such as system noise from the microwave signal receiver, external influences, and internal influences. The results indicate that the system noise is the dominant source of the excessive highfrequency noise. As one method of mitigation, a tighter bandwidth filter was applied to the DOWR processing, resulting in modest improvements in gravity solutions. / text

In this thesis we study classes of static spherically symmetric solutions to the Einstein and Einstein–Maxwell equations that may be used to model the interior of compact stars. We also study the spherical accretion of fluids on to bodies in both general relativity and the Newtonian theory of gravity. The condition for pressure isotropy is obtained upon specifying one of the gravitational potentials and the electric field intensity. A series solution was found after specifying a cubic form for the potential. The pressure and energy density appear to be non–singular and continuous inside the star. This solution admits an explicit equation of state that, in regions close to the stellar centre, may be approximated by a polytrope. Another class of exact solutions to the Einstein–Maxwell solutions was found with charge. These solutions are in the form of hypergeometric functions with two free parameters. For particular parameter values we recovered two previously known exact solutions that are reasonable models for the interior of compact stars. We demonstrated two new solutions for other choices of the parameters. One of these has well behaved pressure, energy density and electric field intensity variables within the star. The other was rejected as unphysical on the grounds that it has a negative energy density. This violates the energy conditions. We obtained the mass accretion rate and critical radius of a polytrope accreting onto a D– dimensional Schwarzschild black hole. The accretion rate, ˙M , is an explicit function of the black hole mass, M, as well as the gas boundary conditions and the dimensionality, D, of the spacetime. We also found the asymptotic compression ratios and temperature profiles below the accretion radius and at the event horizon. This generalises the Newtonian expressions of Giddings and Mangano (2008) which examined the accretion of TeV black holes. We obtained the critical radius and accretion rates of a generalised Chaplygin gas accreting on to body under a Newtonian potential. The accretion rate is about 2 - 4 times greater than that for neutral hydrogen. The Rankine–Hugoniot relations for shocked GCG flow were also found. We found general expressions for the pressure and density compression ratios. Some post shock states imply negative volumes. We suspect that these may be thermodynamically forbidden. / Thesis (Ph.D.)-University of KwaZulu-Natal, Westville, 2012.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis (Ph.D.) - University of St Andrews, September 2008.