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

Introduction Problem Definitions Method Solution Result
In coordinates (x i , τ) the equations for vector multiplet are
[
F 1τ + D 1 , i (
1 + |⃗x|
2 ) ]
Φ 0 − x 3 Φ 9 + x 1 F 12 = 0
2
F 2τ +
[
F 3τ + D 3 , i 2
[
[
D 2 , i (
1 + |⃗x|
2 ) ]
Φ 0 − x 3 Φ 9 − x 2 F 21 = 0
2
(
1 + |⃗x|
2 ) Φ 0 − x 3 Φ 9
]
+ x 1 F 32 − x 2 F 31 = 0
(
1 + |⃗x|
2 ) Φ 0 − x 3 Φ 9
]
+ x 1 F τ2 − x 2 F τ1 = 0
D τ , i 2
[
[Φ 9 , D τ ] + Φ 9 , i (
1 + |⃗x|
2 ) ]
Φ 0 + x 1 [Φ 9 , D 2 ] − x 2 [Φ 9 , D 1 ] = 0
2
Vasily Pestun Localization for ’t Hooft operators on S 4 18/35