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 />
Barnes G-function<br />
The double product can be regularized<br />
G(1 + z) = (2π) z/2 e −((1+γz2 )+z)/2<br />
∞∏<br />
n=1<br />
(<br />
1 + z ) n<br />
e<br />
−z+ z2<br />
2n . (5.5)<br />
n<br />
and then the one-loop contribution from each pole is<br />
Z 1-loop,pole (â) = ∏ ( ) (<br />
α · â<br />
G 1/2 G 1/2 2 + α · â )<br />
ε<br />
ε<br />
α<br />
and recall that the gauge parameter â at the poles is (at θ = 0)<br />
â(N) = ia − B 2r<br />
â(S) = ia + B 2r ,<br />
Vasily Pestun Localization <strong>for</strong> ’t <strong>Hooft</strong> operators on S 4 28/35
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