This thesis is concerned with mathematical interpretations of some recent develop- ments in string theory. All theories are considered before quantisation. The rst half of the thesis investigates a large class of Lagrangians, L, that arise in the physics literature. Noether's famous theorem says that under certain conditions there is a bijective correspondence between the symmetries of L and the \conserved currents" or integrals of motion. The space of integrals of motion form a sheaf and has a bilinear bracket operation. We show that there is a canonical sheaf d1;0 J1( ) that contains a representation of the higher Dorfman bracket. This is the rst step to de ne a Courant algebroid structure on this sheaf. We discuss the existence of this structure proving that, for a re ned de nition, we have the necessary components. The pure spinor formalism of string theory involves the addition of the algebra of pure spinors to the data of the superstring. This algebra is a Koszul algebra and, for physicists, Koszul duality is string/gauge duality. Motivated by this, we investigate the intimate relationship between a commutative Koszul algebra A and its graded Lie superalgebra Koszul dual to A, U(g) = A!. Classically, this means we obtain the algebra of syzygies AS from the cohomology of a Lie subalgebra of g. We prove H (g 2;C) ' AS again and extend it to the notion of k-syzygies, which we de ne as H (g k;C). In particular, we show that H B er(A) ' H (g 3;C), where H Ber(A) is the Berkovits cohomology of A.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

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In this thesis we address the problem of supersymmetry breaking in four dimensional string theory. We derive an effective Lagrangian describing the low energy degrees of freedom including the Goldstone mode associated with the spontaneously broken R-symmetry when a gaugino condensate forms. We show the equivalence between our approach and those previously used for studying gaugino condensate in 4D string theory but we also show the need to include quantum effects due to the strong coupling constant in the hidden sector. We determine the vacuum structure of the complete scalar potential and show that supersymmetry is broken and a large mass hierarchy may develop with a single gaugino condensate. Realistic phenomenological values for the gauge coupling constant, unification scale and soft supersymmetric breaking terms can be obtained. Consistency with the minimal supersymmetric extension of the standard model requires the hidden gauge group to be SU(6) or SO(9).

Thesis (Ph.D.) -- University of Adelaide, School of Chemistry and Physics, Discipline of Physics, 2005. / "March 2005" Includes bibliographical references. Also available in a print form.

Thesis (Ph.D.). / Written for the Dept. of Physics. Title from title page of PDF (viewed 2008/05/08). Includes bibliographical references.

Thesis (M.Sc.). / Written for the Dept. of Physics. Title from title page of PDF (viewed 2008/12/10). Includes bibliographical references.

Thesis (M.Sc.). / Written for the Dept. of Physics. Title from title page of PDF (viewed 2009/06/29). Includes bibliographical references.

Undergraduate honors paper--Mount Holyoke College, 2005. Dept. of Physics. / Includes bibliographical references (leaves 30-31).