Scalar Potential of the Squashed Seven-sphere Stability, the Swampland and Kähler Geometry
Typ
Examensarbete för masterexamen
Program
Physics and astronomy (MPPAS), MSc
Publicerad
2019
Författare
Bergström, Sebastian
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
Finding a consistent theory of quantum gravity has been a long-standing problem in
physics and all attempts made share a common feature: quantum gravitational effects
become important only at very high energies, much higher than the energy scales at
which current particle physics are done. Thus, connecting a particle phenomenological
description to a theory of quantum gravity has proven to be incredibly difficult. A recently
proposed solution to this is known as the Swampland program which aims to construct a
set of conjectures dictating how theories consistent with quantum gravity must behave.
Theories not fulfilling these conjectures are said to lie in the ”swampland”, while consistent
theories are said to lie in the ”landscape”.
In this thesis the compactification of 11-dimensional supergravity on a squashed sevensphere
is studied. This scenario seems to contradict the Non-AdS SUSY conjecture, at
least at a perturbative level, and a better of understanding of it is therefore essential for the
swampland program. A thorough description of the geometry of a squashed seven-sphere
is provided, which then is extended to spacetime dependent parameters of the sphere
described by scalar fields. The stability in terms of these scalars is analysed, which leads
to the contradiction mentioned above. Finally, an attempt to generalise the setup using
complex geometry is done, treating the scalar fields as coordinates on a Kähler manifold. It
is found that a simple and natural coset structure for the Kähler manifold, SL(2,R)/U(1),
might not be the correct ansatz. Hence, further studies of the full 11-dimensional theory
would be beneficial in order to determine the true coset structure.
Beskrivning
Ämne/nyckelord
quantum gravity , supergravity , the swampland , Kähler geometry , the sevensphere