Use this URL to cite or link to this record in EThOS:
Title: Self-duality and extended objects
Author: Robertson, Graeme Donald
ISNI:       0000 0001 3526 5613
Awarding Body: Durham University
Current Institution: Durham University
Date of Award: 1989
Availability of Full Text:
Access from EThOS:
Access from Institution:
In 1986 Polyakov published his theory of rigid string. I investigate the instantons associated with the consequent new fine structure of strings in four dimensional Euclidean space-time. I reduce the self-dual equation of rigid string instantons to a simple form and show that (p,q) torus knots satisfy the equation, thus forming an interesting new class of solutions. I calculate by computer the world-sheet self-intersection number of the first few such closed knotted strings and derive a very simple formula for the self-intersection number of a torus knot. I consider an interpretation in terms of the first Chem number and discover the empirical formula Q = q - p for the inslanton number, Q, of torus knots and links. In 1987 Biran, Floratos and Savvidy pioneered an approach for constructing self-dual equations for membranes. I present some new solutions for self-dual membranes in three dimensions. In 1989 Grabowski and Tze pointed out a new class of exceptional immersions for which self-dual equations can be constructed and for which there are no known non-trivial solutions. By analogy with (p,q) torus knots, I describe an algorithm for generating a class of potential solutions of self-dual lumps in eight dimensions. I show how these come to within a single sign change of solving all the required constraints and come very close to solving all the 32 self-dual (4;8)-brane equations.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: String theory