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Feb 2009

Feb 2013

Topics in locally supersymmetric non-linear sigma models

It is widely thought that a complete picture that resolves at least some of the problems with the standard model (such as the absence of a description of gravity and the well known hierarchy problem) could be described by a supersymmetric extension of the Standard Model. On the other hand, the rapidly growing field of string theory makes use of supersymmetry as a crucial ingredient. Supersymmetric extensions of Einstein's theory of gravity, called (supergravity theories) allow the coupling of matter fields to the gravitational interaction, described by a massless particle of spin 2 (called the graviton). This coupling is made possible due to invariance under local supersymmetry transformations. Non-linear sigma models (NLSMs) have many successful applications in field theory, string theory and statistical mechanics. They appear naturally as low energy effective actions and have a useful geometric interpretation. NLSMs of increasing interest are those possessing supersymmetry. Supersymmetric NLSMs possess an intimate relationship with complex geometry. In particular, NLSMs possessing local N = 2 supersymmetry are related to quaternion metrics of a quaternion Kähler manifold. This project is aimed at exploring the applications of a recently found projective superspace formulation for 4D N = 2 matter-coupled supergravity (hep-th/0805.4683). This research project aims to derive new quaternion Kähler metrics and explore some of their applications to black hole physics.

The construction of new quaternion metrics have a number of applications in string theory such as for the Bekenstein-Hawking entropy for 4D N = 2 supersymmetric BPS black holes.

- Hackett Scholarship