Towards a mathematical definition of Coulomb branches of 3-dimensional N=4 gauge theories
Event details
| Date | 25.03.2015 |
| Hour | 13:15 › 15:00 |
| Speaker | Hiraku Nakajima, RIMS Kyoto |
| Location | |
| Category | Conferences - Seminars |
(Note the unusual time and place)
Consider the 3-dimensional N=4 supersymmetric gauge
theory associated with a compact Lie group G and its quaternionic
representation M. Physicists study its Coulomb branch, which
is a noncompact hyper-Kähler manifold, such as instanton moduli
spaces on R^4, SU(2)-monopole moduli spaces on R^3, etc.
In this talk, we propose two mathematical definitions of the coordinate
ring of the Coulomb branch, using a) the vanishing cycle cohomology group
of a certain moduli space for a gauged sigma-model on the 2-sphere
associated with (G,M), and b) the Borel-Moore homology group
of a similar moduli space related with the affine Grassmannian of G.
Consider the 3-dimensional N=4 supersymmetric gauge
theory associated with a compact Lie group G and its quaternionic
representation M. Physicists study its Coulomb branch, which
is a noncompact hyper-Kähler manifold, such as instanton moduli
spaces on R^4, SU(2)-monopole moduli spaces on R^3, etc.
In this talk, we propose two mathematical definitions of the coordinate
ring of the Coulomb branch, using a) the vanishing cycle cohomology group
of a certain moduli space for a gauged sigma-model on the 2-sphere
associated with (G,M), and b) the Borel-Moore homology group
of a similar moduli space related with the affine Grassmannian of G.
Practical information
- Informed public
- Free