Abstract
This thesis will present work completed throughout the course of my doctoral studies. The thesis primarily concerns developments in the theories of the M5brane and systems of multiple Mbranes in Mtheory.Theories of multiple M2branes 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 M5brane however remains shrouded in mystery. A basic multiplet for a single M5brane is known but scant else directly; it is believed that the sixdimensional (2, 0) model describes the worldvolume theory for multiple M5branes, 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 Dbranes. Interspersed are diversions into topics which are of relevance for the later work such as the notion of KaluzaKlein compactiﬁcation, BPS states, and solitons. I then discuss how String Theory leads inexorably to Mtheory and discuss the basics of this new theory. Following this, I dive deeper into a detailed discussion of the BLG theory describing pairs of M2branes. Next, I move into more recent and tentative models of multiple Mbranes which emerge from attempts to extend the (2, 0) algebra to a nonabelian generalisation. This typically involves the addition of nondynamical 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 nonabelian extended (2, 0) theory has a natural sector within it which describes ‘null’ M2branes. 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 nonLorentzian ﬁeld theory. Another such lagrangian is also found which comes from another extended (2, 0) system.
Finally, I discuss a system of M5branes wrapped on the multiTaubNUT geometry. This system has a natural string theory interpretation of intersecting D4 and D6branes. Such a brane conﬁguration is known to contain chiral fermions which propagate along the intersection and which arise due to the open strings stretching between the branes. This picture has been previously poorly understood from the Mtheory perspective; this work shows the Mtheory origin of the chiral states and argues that they are described by a WessZuminoWittenlike model.
Date of Award  2019 

Original language  English 
Awarding Institution 

Supervisor  Neil Lambert (Supervisor) & Sakura SchaferNameki (Supervisor) 