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 />
Supersymmetric Wilson loop<br />
∮<br />
W R (C) = tr R Pexp (Adx + iΦ 0 ds)<br />
Supersymmetric ’t <strong>Hooft</strong> loop<br />
Specify asymptotics <strong>in</strong> local R 3 normal to the loop (x = 0):<br />
F A → − ⋆ B dx<br />
2 x 2 , x → 0<br />
Φ 9 → B 1<br />
2 x , x → 0<br />
The parameter is B ∈ g (weight of ∨ G) def<strong>in</strong><strong>in</strong>g homomorphism<br />
U(1) → G.<br />
The asymptotics locally satisfies Bogomolny equations<br />
C<br />
D A Φ 9 = ⋆F A<br />
Vasily Pestun Localization <strong>for</strong> ’t <strong>Hooft</strong> operators on S 4 9/35