Item – Theses Canada

OCLC number
Link(s) to full text
LAC copy
Errasti Diez, Veronica,author.
From M-theory to knot theory via topological field theory /Veronica Errasti Diez.
Ph. D. -- McGill University, 2018
[Montreal] :McGill University Libraries,[2018]
1 online resource
Thesis supervisor: Keshav Dasgupta (Supervisor).
Includes bibliographical references.
"We construct two M-Theory models and relate them to each other through a series of dualities. In doing so, we provide a unifying scheme of the supergravity proposals by Ooguri-Vafa and Witten to study knots and their invariants. Subsequently, we focus in the world-volume gauge theory following from one of the constructed models. This is a four-dimensional, N=4 Yang-Mills theory with generic gauge group SU(N), in the presence of a boundary. We obtain its Hamiltonian and, for time-independent field configurations, we find that the equations of motion minimizing its energy are specific Hitchin integrable systems, along with certain consistency conditions. All these results were first derived by Kapustin-Witten applying localization techniques to the path integral formulation of the gauge theory. Hence, our model provides a simplified scenario for calculations. Additionally, it allows for an interpretation of all the parameters in the theory in terms of supergravity quantities. We also derive the corresponding half-BPS boundary conditions. Upon a topological twist, we show that the boundary physics is governed by a complexified Chern-Simons action, thus providing a suitable subspace for the embedding of knots in our setup. Finally, we include knots in our model. At the M-Theoretical level, this is achieved by adding a given M2-brane state to the previously constructed model. In the bulk of the associated gauge theory, this M2-brane can be understood as a surface operator, whereas in the boundary it appears as a Wilson loop."--
Other link(s)