Friday, February 10, 2012

1202.1956 (Johan Kallen et al.)

Twisted supersymmetric 5D Yang-Mills theory and contact geometry    [PDF]

Johan Kallen, Maxim Zabzine
We extend the localization calculation of the 3D Chern-Simons partition
function over Seifert manifolds to an analogous calculation in five dimensions.
We construct a twisted version of N=1 supersymmetric Yang-Mills theory defined
on a circle bundle over a four dimensional symplectic manifold. The notion of
contact geometry plays a crucial role in the construction and we suggest a
generalization of the instanton equations to five dimensional contact
manifolds. Our main result is a calculation of the full perturbative partition
function on a five sphere for the twisted supersymmetric Yang-Mills theory with
different Chern-Simons couplings. The final answer is given in terms of a
matrix model. Our construction admits generalizations to higher dimensional
contact manifolds. This work is inspired by the work of Baulieu-Losev-Nekrasov
from the mid 90's, and in a way it is covariantization of their ideas for a
contact manifold.
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