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

Introduction Problem Definitions Method Solution Result
Technical details:
Convenient coordinates
S 4 = S 1 × B 3
where B 3 is a 3d solid ball with a boundary B 3 : ∑ 3
i=1 x2 i < 1
and S 1 is a circle τ
The round S 4 metric is
ds 2 =
dx 2 i
(1 + x 2 ) 2 + (1 − x2 ) 2
(1 + x 2 ) 2 dτ 2
B 3 -flat rescaled metric
ds 2 = dx 2 i + (1 − x 2 ) 2 dτ 2
The ’t Hooft loop is the S 1 fiber at x i = 0.
The North pole, the first fixed point of Q 2 is x = (0, 0, 1)
he South pole, the second fixed of Q 2 is x = (0, 0, −1)
Vasily Pestun Localization for ’t Hooft operators on S 4 17/35