AbstractThis thesis will present work completed throughout the course of my doctoral studies. The thesis primarily concerns developments in the theories of the M5-brane and systems of multiple M-branes in M-theory.
Theories of multiple M2-branes are currently well understood, with the BLG and ABJM models providing a comprehensive and rich base from which to continue study of such objects. The M5-brane however remains shrouded in mystery. A basic multiplet for a single M5-brane is known but scant else directly; it is believed that the six-dimensional (2, 0) model describes the worldvolume theory for multiple M5-branes, however this theory is itself poorly understood. There is therefore much work to be done to gain a deeper understanding of these objects and how they interact. This thesis hopes to be a small part of that story.
In the ﬁrst part of this thesis I provide an extended introduction, giving a broad background to many of the topics discussed later in the text. This is intended to set the scene and introduce the major players for what is to follow. I discuss the development of String Theory and its basic results including the spectrum, dualities, and D-branes. Interspersed are diversions into topics which are of relevance for the later work such as the notion of Kaluza-Klein compactiﬁcation, BPS states, and solitons. I then discuss how String Theory leads inexorably to M-theory and discuss the basics of this new theory. Following this, I dive deeper into a detailed discussion of the BLG theory describing pairs of M2-branes. Next, I move into more recent and tentative models of multiple M-branes which emerge from attempts to extend the (2, 0) algebra to a non-abelian generalisation. This typically involves the addition of non-dynamical form ﬁelds into the model which allow for various diﬀerent brane conﬁguration interpretations.
I then begin describing the novel systems which constitute my contribution to the ﬁeld. Firstly, I show how the non-abelian extended (2, 0) theory has a natural sector within it which describes ‘null’ M2-branes. This system is analysed and is shown to reduce to motion on the moduli space of solutions to the Hitchin system. From this I then ﬁnd an action for this system which provides a concrete example of a maximally symmetric non-Lorentzian ﬁeld theory. Another such lagrangian is also found which comes from another extended (2, 0) system.
Finally, I discuss a system of M5-branes wrapped on the multi-Taub-NUT geometry. This system has a natural string theory interpretation of intersecting D4 and D6-branes. Such a brane conﬁguration is known to contain chiral fermions which propagate along the inter-section and which arise due to the open strings stretching between the branes. This picture has been previously poorly understood from the M-theory perspective; this work shows the M-theory origin of the chiral states and argues that they are described by a Wess-Zumino-Witten-like model.
|Date of Award
|Neil Lambert (Supervisor) & Sakura Schafer-Nameki (Supervisor)