Marcos MARIŅO
(CERN)
Chern-Simons Theory and Enumerative Geometry
The goal of these lectures is to give
an introduction to the relations between
enumerative geometry of non-compact, toric
Calabi-Yau manifolds, and Chern-Simons theory.
I will start with an introduction to the relevant
aspects of Chern-Simons theory and its large N
expansion. Then, I will explain the realization of
Chern-Simons theory on the three-sphere
in terms of closed and open
topological strings, as well as the important idea
of large N or geometric transition. Finally, I will
extend this framework in order to compute topological
string amplitudes of general toric manifolds using Chern-Simons
ingredients.
References
Lecture Notes:
Other References:
-
M. Mariņo,
``Enumerative geometry and knot invariants,''
arXiv:hep-th/0210145.
- R. Gopakumar and C. Vafa,
``On the gauge theory/geometry correspondence,''
Adv. Theor. Math. Phys. 3, 1415 (1999)
[arXiv:hep-th/9811131].
- M. Aganagic, M. Mariņo and C. Vafa,
``All loop topological string amplitudes from Chern-Simons theory,''
arXiv:hep-th/0206164.