U-dualities in Type II string theories and M-theory.
Abstract
In this thesis the recently developed duality covariant approach to string and Mtheory
is investigated. In this formalism the U-duality symmetry of M-theory or Tduality
symmetry of Type II string theory becomes manifest upon extending coordinates
that describe a background.
The effective potential of Double Field Theory is formulated only up to a boundary
term and thus does not capture possible topological effects that may come from a
boundary. By introducing a generalised normal we derive a manifestly duality covariant
boundary term that reproduces the known Gibbons-Hawking action of General Relativity,
if the section condition is imposed. It is shown that the full potential can be
represented as a sum of the scalar potential of gauged supergravity and a topological
term that is a full derivative. The latter is written totally in terms of the geometric
flux and the non-geometric Q-flux integrated over the doubled torus.
Next we show that the Scherk-Schwarz reduction of M-theory extended geometry
successfully reproduces known structures of maximal gauged supergravities. Local symmetries
of the extended space defined by a generalised Lie derivatives reduce to gauge
transformations and lead to the embedding tensor written in terms of twist matrices.
The scalar potential of maximal gauged supergravity that follows from the effective potential
is shown to be duality invariant with no need of section condition. Instead, this
condition, that assures the closure of the algebra of generalised diffeomorphisms, takes
the form of the quadratic constraints on the embedding tensor.
Authors
Musaev, Edvard T.Collections
- Theses [3711]