AbstractM-theory is well-known but not well-understood. It arises as an umbrella theory that unifies the various perturbative string theories into a single nonperturbative theory. In its strong coupling phase M-theory does not possess string states but rather M2-branes and M5-branes. The purpose of this thesis is to explore the properties of multiple coincident M2- and M5-branes. It is based on the author’s papers [1, 2] (in collaboration with Neil Lambert),  (in collaboration with Imtak Jeon and Neil Lambert) and . We begin with a review of the construction of three-dimensional J\f = 8 and J\i = 6 super-symmetric Chern-Simons-matter theories. These include the BLG and ABJM models of multiple M2-branes and our focus will be on their formulation in terms of 3-algebras. We then examine the coupling of multiple M2-branes to the background 3-form and 6-form gauge fields of eleven-dimensional supergravity. In particular we show in detail how a natural generalisation of the Myers flux-terms, along with the resulting curvature of the background metric, leads to mass terms m the effective field theory. Working to lowest nontrivial order in fermions, we demonstrate the supersymmetric invariance of the four-derivative order corrected Lagrangian of the Euclidean BLG theory and determine the theory’s higher derivative corrected supersymmetry transformations. The supersymmetry algebra is also shown to close on the scalar and gauge fields. We also consider periodic arrays of M2-branes in the ABJM model in the spirit of a circle compactification to D2-branes in type IIA string theory. The result is a curious formulation of three-dimensional maximally supersymmetric Yang-Mills theory. Upon further T-duality on a transverse torus we obtain a non-manifest-Lorentz-invariant description of five-dimensional maxi¬mally supersymmetric Yang-Mills which can be viewed as an M-theory description of M5-branes on T3.
After reviewing work to describe multiple M5-branes using 3-algebras we show how the re-sulting novel system of equations reduces to one-dimensional motion on instanton moduli space. Quantisation leads to the previous light-cone proposal of the (2,0) theory, generalised to include a potential that arises on the Coulomb branch as well as couplings to background gauge and self-dual 2-form fields.
|Date of Award
|1 Dec 2012
|Neil Lambert (Supervisor) & Peter West (Supervisor)