Strings as Sigma Models and in the Tensionless Limit

The magnetic and structural properties of nano magnet arrays and ferromagnetic thin films are investigated. Circular x-rays are used and extensive use is made in this Thesis of the X-ray Magnetic Circular Dichroism (XMCD) technique. By means of the XMCD magneto-optic sum rules the values of the orbital and spin moments are determined. In the case of the nano magnet arrays studied, the XMCD technique is used in a spatially resolved mode using Photo Electron Emission Microscopy (PEEM) after circular light excitation. The Extended X-ray Absorption Fine Structure (EXAFS) is studied in both the Co K- and L-edges.In situ Co L-edge X-ray XMCD spectroscopy measurements are presented, in combination with spectro-microscopy results, on Co/Pt and Co/Au based nano-dot arrays, of typical dot lateral size 250×100 nm2, on self organized Si0.5Ge0.5. The Co is only a few atomic layers thick. The dot arrays display a high degree of lateral order and the individual dots, in several cases, exhibit a stable magnetic moment at 300 K. It is found possible to characterize the spin reorientation of these dot arrays…


1 Introduction in Swedish
2 Introduction
3 Basic string theory
3.1 Bosonic strings
3.1.1 Invariances
3.1.2 Classical equations of motion
3.1.3 The closed string
3.1.4 The open string
3.1.5 Different methods of quantization
3.1.6 Oriented vs. unoriented strings
3.1.7 String interactions and vertex operators
3.2 Backgrounds
3.3 Superstrings
3.3.1 Supersymmetry
3.3.2 World-sheet supersymmetry
3.3.3 Quantization
3.3.4 Space-time supersymmetry
3.3.5 Five different but equal theories
3.3.6 Green-Schwarz superstrings
4 The tensionless limit of string theory
4.1 Massive and massless relativistic particles
4.2 The tensionless limit of string theory
4.3 Gravitational field of a massless relativistic point particle
4.4 A background for type IIB string theory
4.5 A background of a tensionless string
5 Strings in a pp-wave background
5.1 The pp-wave background as a limit
5.2 Ordinary string in a pp-wave background
5.3 Tensionless string in a pp-wave background
6 Extended supersymmetry and geometry
6.1 The N =(p,q) formulation
6.2 A non-linear sigma model
6.3 Extended supersymmetry
6.4 Complex geometry
6.5 Geometrical interpretation
6.6 Generalized complex geometry
6.7 Hamiltonian formulation
6.7.1 Generalized Kähler from a sigma model
6.7.2 Generalized hyperKähler from a sigma model
6.8 Manifest N =(2,2) formulation
7 T-duality and extended supersymmetry
7.1 T-duality as a canonical transformation
7.2 T-duality as a gauging of the isometry
7.3 T-duality as a symplectomorphism
7.4 Extended supersymmetry in the T-dual model
8 First order sigma model and extended supersymmetry
8.1 The sigma model
8.2 The supersymmetry transformation
9 Epilogue
Appendix A: Conditions from the supersymmetry algebra
A.1 Variation of the action
A.2 N =(2,1) commutators
A.3 N =(2,2) commutators

Author: Persson, Andreas

Source: Uppsala University Library

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