Exact Results for 't Hooft Loops in Gauge Theories ... - Solvay Institutes
Exact Results for 't Hooft Loops in Gauge Theories ... - Solvay Institutes
Exact Results for 't Hooft Loops in Gauge Theories ... - Solvay Institutes
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Introduction Problem Def<strong>in</strong>itions Method Solution Result<br />
In coord<strong>in</strong>ates (x i , τ) the equations <strong>for</strong> vector multiplet are<br />
[<br />
F 1τ + D 1 , i (<br />
1 + |⃗x|<br />
2 ) ]<br />
Φ 0 − x 3 Φ 9 + x 1 F 12 = 0<br />
2<br />
F 2τ +<br />
[<br />
F 3τ + D 3 , i 2<br />
[<br />
[<br />
D 2 , i (<br />
1 + |⃗x|<br />
2 ) ]<br />
Φ 0 − x 3 Φ 9 − x 2 F 21 = 0<br />
2<br />
(<br />
1 + |⃗x|<br />
2 ) Φ 0 − x 3 Φ 9<br />
]<br />
+ x 1 F 32 − x 2 F 31 = 0<br />
(<br />
1 + |⃗x|<br />
2 ) Φ 0 − x 3 Φ 9<br />
]<br />
+ x 1 F τ2 − x 2 F τ1 = 0<br />
D τ , i 2<br />
[<br />
[Φ 9 , D τ ] + Φ 9 , i (<br />
1 + |⃗x|<br />
2 ) ]<br />
Φ 0 + x 1 [Φ 9 , D 2 ] − x 2 [Φ 9 , D 1 ] = 0<br />
2<br />
Vasily Pestun Localization <strong>for</strong> ’t <strong>Hooft</strong> operators on S 4 18/35