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 />
Wilson operators<br />
1. Def<strong>in</strong>e N = 2 theory on S 4 of radius r.<br />
2. Localize the path <strong>in</strong>tegral and get [V.P.’07]<br />
〈W R (C)〉 S 4 = 1 ∫<br />
[da]|Z Ω (ia, ɛ 1 , ɛ 2 , m, τ)| 2 tr R e 2πiar<br />
Z S 4<br />
Z Ω – Nekrasov’s partition function of N = 2 twisted theory on<br />
R 4 ɛ 1 ,ɛ 2<br />
[Losev-Moore-Nekrasov-Shatashvili’95,Nekrasov’02]<br />
ɛ 1 = ɛ 2 = 1/r<br />
Vasily Pestun Localization <strong>for</strong> ’t <strong>Hooft</strong> operators on S 4 5/35