Mathematical Physics Learning Seminar
Gopakumar-Vafa conjectures and large
N-dualities
The Gopakumar-Vafa conjectures relate quantum invariants of
knots and 3-manifolds (eg. Jones and HOMFLY polynomials) to Gromov-Witten
invariants of Calabi-Yau three-folds. The conjecture arises from taking
Chern-Simons theory with gauge group SU(N). In the large N limit this
gauge theory looks (perturbatively) like open topological string theory on
a certain Calabi-Yau three-fold. A transition converts this to closed
topological string theory on a related Calabi-Yau.
This year (2003-2004) we will run a learning seminar on this
topic, aiming to cover the background knowledge necessary to
understand the conjecture. This will include:
- Chern-Simons theory, TQFTs, perturbative expansions, quantum
invariants,
- Gromov-Witten invariants (closed and open), BPS states,
- geometry of Calabi-Yau 3-folds, resolving and smoothing
singularities.
Some relevant references are:
- Vafa and co-authors :
hep-th/9809187,
hep-th/9811131,
hep-th/9812127,
hep-th/9912123,
hep-th/0010102,
hep-th/0008142,
hep-th/0011256,
hep-th/0012136,
hep-th/0108064,
hep-th/0110171,
hep-th/0205297,
hep-th/0206164,
hep-th/0211098
- Marino's survey :
hep-th/0210145
- Grassi and Rossi's survey (probably the most mathematical
description currently available) :
math.AG/0209044
- Witten "Chern-Simons gauge theory as a string theory" :
hep-th/9207094
- Taubes "Lagrangians for the Gopakumar-Vafa conjecture" :
math.DG/0201219
Spring 2004 schedule:
- 11th February - Justin Sawon "Large N duality overview I"
- 25th February - Justin Sawon "Large N duality overview II"
Fall 2003 schedule:
- 24th September - Justin Sawon "Introductory and organizational
seminar"
- 1st October - Alexander Kirillov "Chern-Simons theory I :
non-perturbative approach"
- 8th October - Alexander Kirillov "Chern-Simons theory II :
non-perturbative approach (continued)"
- 29th October - Justin Sawon "Chern-Simons theory III :
perturbative approach"
- 5th November - Alexander Kirillov "Feynman diagrams for matrix
models and ribbon graphs"
- 12th November - Alexander Kirillov "Random matrices : Large N
limit and planar diagrams"
- 3rd December - Justin Sawon "Chern-Simons theory IV :
perturbative approach (continued)"
Seminars will be held in room 5-127 at 4pm Wednesday. Please visit
the calendar
of events to find the next talk.
Back to the main page.
This page last modified
by Justin Sawon
Sunday, 22-Feb-2004 15:15:52 MST
Email corrections and comments to
sawon@math.sunysb.edu