Mirror symmetry at genus one of elliptic curves
Typ
Examensarbete för masterexamen
Program
Engineering mathematics and computational science (MPENM), MSc
Publicerad
2020
Författare
Fries, Magnus
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
This master's thesis is concerned with mirror symmetry at genus one
for elliptic curves. Mirror symmetry stems from string theory in physics
and conjectures a relation between the symplectic (the A-model) and
complex structures (the B-model) of a Calabi-Yau manifold and its
mirror manifold. At genus one, the B-model calculation can be defined
using analytic torsion introduced by Bershadsky, Cecotti, Ooguri and
Vafa. For elliptic curves, this is calculated using the Kronecker limit
formula, which is also derived in detail. The A-model is concerned with
the generating series of genus one Gromov-Witten invariants which is
also calculated for elliptic curves. Then the mirror symmetry correspon-
dence is shown using the derivatives of the A- and B-model calculations.