Supermultiplets and Koszul Duality
Typ
Examensarbete för masterexamen
Program
Publicerad
2021
Författare
Jonsson, Simon
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
There is a deep and general correspondence connecting constrained objects, superalgebras
and supermultiplets. The most natural way of displaying this correspondence is using
partition functions and BRST formalism. The partition functions of the constrained objects
can be found to be dual to that of a Lie superalgebra and in some cases L1 algebras. The
duality reveals itself through the partition functions being each others inverses.
We find the pure spinor partition functions in D = 10 to contain the supermultiplet for
D = 10 linearised super-Yang-Mills. We find the dual algebra to be an extension of D5 with
an odd null root, defining an infinite dimensional graded Lie superalgebra called a Borcherds
superalgebra. The algebra is proven to be freely generated by the super-Yang-Mills multiplet
from order 3.
Further investigation concerns the case of D = 11 supergravity. The dual algebra is no
longer just a Lie superalgebra. In addition to the Lie bracket structure there is also, at least,
a 3- and a 4-bracket structure. It is conjectured that this algebra, from order 4, is freely
generated, under the Lie bracket, by the D = 11 supergravity multiplet.
Beskrivning
Ämne/nyckelord
Representation theory , pure spinors , supersymmetry , Lie superalgebras , partition functions, , super-Yang-Mills , supergravity