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 />
S-duality<br />
F<strong>in</strong>ally, let us compare our <strong>for</strong>mulae <strong>for</strong> Wilson and ’t <strong>Hooft</strong><br />
loops and<br />
∫<br />
〈 〉<br />
ZW (R) τ = [da]|Z north (ia, τ)| ∑ 2 e 2πiaw<br />
w<br />
〈<br />
ZT (B)<br />
〉<br />
τ = ∫<br />
da<br />
∣ Z north(ia − B ∣ ∣∣∣<br />
2<br />
2 , τ) · Z equator (ia)<br />
Notice:<br />
Wilson loop of weight w <strong>in</strong>serts operator exp(2πiwa)<br />
t’ <strong>Hooft</strong> loop of coweight B <strong>in</strong>serts shift operator exp(B ∂<br />
∂a )<br />
Hence, the latter <strong>for</strong>mula (magnetic) at τ ∨ = − 1 τ<br />
is Fourier<br />
trans<strong>for</strong>m of the <strong>for</strong>mer (electric).<br />
Vasily Pestun Localization <strong>for</strong> ’t <strong>Hooft</strong> operators on S 4 34/35
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