Symmetry and holonomy in M Theory

In this dissertation, we study the generalized symmetries in supergravities and superconformal field theories from the string theory perspective. Part one is devoted to the study of string universality in high spacetime dimensions. Answering this question requires us to combine the following two approaches. In the "top-down" approach, We focus on supergravity theories in 7, 8, and 9 dimensional spacetime with 16 supercharges. We emphasize two discrete aspects of these theor...

In the strong coupling limit type IIA superstring theory develops an eleventh dimension that is not apparent in perturbation theory. This suggests the existence of a consistent 11d quantum theory, called M theory, which is approximated by 11d supergravity at low energies. In this review we describe some of the evidence for this picture and some of its implications.

In relation to the superspace modifications of 11D supergeometry required to describe the M-theory low-energy effective action, we present an analysis of infinitesimal supergravity fluctuations about the flat superspace limit. Our investigation confirms Howe's interpretation of our previous Bianchi identity analysis. However, the analysis also shows that should 11D supergravity obey the rules of other off-shell supergravity theories, the complete M-theory corrections will nec...

Eleven-dimensional supergravity reveals large exceptional symmetries upon reduction, in accordance with the U-duality groups of M-theory, but their higher-dimensional geometric origin has remained a mystery. In this letter, we show that D=11 supergravity can be extended to be fully covariant under the exceptional groups E_{n(n)}, n=6,7,8. Motivated by a similar formulation of double field theory we introduce an extended `exceptional spacetime'. We illustrate the construction ...

In this paper we study eleven-dimensional supergravity in its most general form. This is done by implementing manifest supersymmetry (and Lorentz invariance) through the use of the geometric (torsion and curvature) superspace Bianchi identities. These identities are solved to linear order in a deformation parameter introduced via the dimension zero supertorsion given in its most general form. The theory so obtained is referred to as the deformed theory (to avoid the previousl...

In this talk I will survey some of the basic facts about superstring theories in 10 dimensions and the dualities that relate them to M theory in 11 dimensions. Then I will mention some important unresolved issues.

Invited talk at the conference "Fundamental Interactions: From Symmetries to Black Holes" in honor of Francois Englert, 24 - 27 March, Universite Libre de Bruxelles, Belgium

We reformulate eleven-dimensional supergravity, including fermions, in terms of generalised geometry, for spacetimes that are warped products of Minkowski space with a $d$-dimensional manifold $M$ with $d\leq7$. The reformation has a $E_{d(d)} \times \mathbb{R}^+$ structure group and is has a local $\tilde{H}_d$ symmetry, where $\tilde{H}_d$ is the double cover of the maximally compact subgroup of $E_{d(d)}$. The bosonic degrees for freedom unify into a generalised metric, an...

In this thesis we summarize the reformulation of the bosonic sector of eleven dimensional supergravity as a simultaneous nonlinear realisation based on the conformal group and an enlarged affine group called G11. The vielbein and the gauge fields of the theory appear as space-time dependent parameters of the coset representatives. Inside the corresponding algebra g11 we find the Borel subalgebra of e7, whereas performing the same procedure for the Borel subalgebra of e8 we ha...

This thesis firstly investigates whether D=11 supergravity can be lifted to a higher dimensional theory without introducing additional bosonic fields by interpreting the E(7(7))-symmetry of N=8 d=4 supergravity as part of a coordinate symmetry acting in a 60 dimensional restricted or exceptional geometry. It is proved that the supersymmetry variations of D=11 supergravity, truncated to d=7, can be reproduced from this exceptional geometry in the expected manner. Secondly, Bor...