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 />
North (South) pole<br />
Near the North pole the operator D, def<strong>in</strong><strong>in</strong>g the equations, is<br />
the self-dual operator<br />
The <strong>in</strong>dex is then<br />
D SD : Ω 1 d∗ ⊕d +<br />
−→ Ω 0 ⊕ Ω 2+<br />
<strong>in</strong>d(D SD,C )(t 1 , t 2 ) = (t 1t 2 + t −1<br />
1 t−1 2 + 2) − (t 1 + t −1<br />
1 + t 2 + t −1<br />
2 )<br />
(1 − t 1 )(1 − t −1<br />
1 )(1 − t 2)(1 − t −1<br />
2 )<br />
1 + t 1 t 2<br />
=<br />
(1 − t 1 )(1 − t 2 ) . (5.1)<br />
<strong>for</strong> the U(1) action z 1 → t 1 z 1 , z 2 → t 2 z 2 .<br />
Vasily Pestun Localization <strong>for</strong> ’t <strong>Hooft</strong> operators on S 4 26/35