Exact Results for 't Hooft Loops in Gauge Theories ... - Solvay Institutes

Introduction Problem Definitions Method Solution Result
When we tensor product sections with the adjoint
representation of G the index becomes (at t i = e iε i
)
ind(D)(ε 1 , ε 2 , â) =
To read the R weights we expand
1 + e iε 1
e iε 2
(1 − e iε 1 )(1 − e iε 2)
= ∑
(1 + e iε 1+iε 2
) ∑
2(1 − e iε 1 )(1 − e iε 2)
n 1 ,n 2 ≥0
w∈adj
e iw·â . (5.2)
(1 + e iε 1
e iε 2
)e in 1ε 1
e in 2ε 2
(5.3)
Therefore, the one-loop contribution from the pole is
∏
[n 1 ε 1 + n 2 ε 2 + α · â] 1/2 [(n 1 + 1)ε 1 + (n 2 + 1)ε 2 + α · â] 1/2 .
n 1 ,n 2 ≥0
(5.4)
Vasily Pestun Localization for ’t Hooft operators on S 4 27/35