Off-shell, maximal supersymmetry & exceptional geometry ANNA KARLSSON

122 Pages·2015·0.73 MB·English

THESIS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
Off-shell, maximal supersymmetry
&
exceptional geometry
ANNA KARLSSON
DepartmentofFundamentalPhysics
CHALMERS UNIVERSITY OF TECHNOLOGY
Go¨teborg,Sweden2015
Off-shell, maximal supersymmetry & exceptional geometry
ANNAKARLSSON
ISBN978-91-7597-230-5
c AnnaKarlsson,2015
(cid:13)
DoktorsavhandlingarvidChalmerstekniskaho¨gskola
Nyserienr3911
ISSN0346-718X
DepartmentofFundamentalPhysics
ChalmersUniversityofTechnology
SE–41296Go¨teborg,Sweden
Phone:[phone]
PrintedbyChalmersReproservice
ChalmersUniversityofTechnology
Go¨teborg,Sweden2015
iii
Off-shell, maximal supersymmetry & exceptional geometry
ANNAKARLSSON
DepartmentofFundamentalPhysics
ChalmersUniversityofTechnology
Abstract
Two lines of research are presented in this thesis, both with a focus on funda-
mental properties within the supersymmetric theories of high energy physics.
The first features analyses based on the actions for maximal supersymmetric
Yang–Mills theory and supergravity, provided by the pure spinor formalism.
Thesecondisthedevelopmentofthetheoryofexceptionalgeometry.
The analyses within maximally supersymmetric Yang–Mills theory and super-
gravity, benefitting from the pure spinor formalism, centres around the inves-
tigations of the UV divergences of the amplitude diagrams, where the case of
maximal supergravity is subject to ongoing research. There is currently an in-
teresting development in connection to the four-dimensional theory, regarding
a possible finiteness, indicated in the pure spinor formalism setting of the re-
search articles appended to this thesis. The results are contrary to the expected
divergence,currentlyofamplitudediagramswithmorethansixloops.
Exceptional geometry is an extension of supergravity that is constructed to in-
corporate U-duality. It is a geometric formulation with an extended space, in a
way similar to in doubled geometry, where T-duality is the symmetry accom-
modated for. Constituting a rather recent area of research, the theory is under
development with respect to the inherent symmetries, the tensor formalism,
etc.,regardingthepropertiesaffectedbytheextendedspace.Itsrecognisedfea-
tures, construction and concepts to be investigated are the objects of interest in
thisthesis.
Keywords:Maximalsupersymmetry,maximalsupergravity,purespinors,loop
amplitudes,exceptionalgeometry,U-duality,highenergyparticlephysics

v
List of appended research papers
Thisthesisisbasedontheworkcontainedinthefollowingpublications,
referredtobyRomannumeralsinthetext.
I. PurespinorsuperfieldsandBorn–Infeldtheory
M.CederwallandA.Karlsson
J.HighEnergyPhys.11(2011)134
arXiv:1109.0809[hep-th]
II. Loopamplitudesinmaximalsupergravitywithmanifestsupersymmetry
M.CederwallandA.Karlsson
J.HighEnergyPhys.03(2013)114
arXiv:1212.5175[hep-th]
III. Exceptionalgeometryandtensorfields
M.Cederwall,J.EdlundandA.Karlsson
J.HighEnergyPhys.07(2013)028
arXiv:1302.6736[hep-th]
IV. Ultravioletdivergencesinmaximalsupergravityfromapurespinorpoint
ofview
A.Karlsson
J.HighEnergyPhys.04(2015)165
arXiv:1412.5983[hep-th]
V. Pure spinor indications of ultraviolet finiteness in D = 4 maximal super-
gravity
A.Karlsson
arXiv:1506.07505[hep-th]
Other publications
I have also written the following conference contribution, not included in this
thesis:
Loopamplitudediagramsinmanifest,maximalsupergravity
•
A.Karlsson
SpringerProc.Phys.153(2014)95
Ongoingresearchprojectsarementionedinchapter1,4and5.

vii
Acknowledgements
Thankyou,
to my supervisor, Martin Cederwall, for being so inspiring and warm-hearted,
andhavingsuchagreatsenseofhumour,
tomymotherandlategrandmother,forbelievinginme,
to family, friends and colleagues that have been there for me in different ways,
sometimeslighteningupmyeveryday,
and to Johanna and Anton, for your helpful comments on the drafts of this
thesis.
Anna

Tomymother
&grandparents