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 />
Smooth solutions<br />
The only topologically trivial solution and smooth away from<br />
s<strong>in</strong>gularity is<br />
x i<br />
F jk = − B 2 ɛ ijk<br />
|⃗x| 3 , F iˆ4 = −ig2 θ B x i<br />
16π 2 |⃗x| 3 ,<br />
Φ 9 =<br />
B<br />
2|⃗x| , Φ 0 = −g 2 θ B 1<br />
16π 2 |⃗x| + a<br />
,<br />
1 + |⃗x|2<br />
4r 2<br />
a/r<br />
K 3 = −(<br />
) 2<br />
,<br />
1 + |⃗x|2<br />
4r 2<br />
The moduli space of solutions is parametrized by a ∈ g.<br />
The path <strong>in</strong>tegral localizes to<br />
Y 0 = g<br />
Vasily Pestun Localization <strong>for</strong> ’t <strong>Hooft</strong> operators on S 4 21/35
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