Exact Results for 't Hooft Loops in Gauge Theories ... - Solvay Institutes

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Introduction Problem Definitions Method Solution Result Method: Localization Principle Localize the path integral: ∫ Z 0 = [Dφ] e −S 0[φ] S 0 – the physical action Q – global fermionic symmetry, QS 0 = 0 Q 2 = R – global bosonic symmetry Deform the action assuming {Q 2 , V } = 0 S t [φ] = S 0 [φ] + t{Q, V } Vasily Pestun Localization for ’t Hooft operators on S 4 10/35
Introduction Problem Definitions Method Solution Result Now consider Integrating by parts we get ∫ Z t = [Dφ] e −S 0[φ]−t{Q,V [φ]} d dt Z t = 0 =⇒ Z 0 = Z ∞ At t = ∞ the one-loop approximation to Z t is exact. But Z t = Z 0 . Hence we get exact Z 0 . Vasily Pestun Localization for ’t Hooft operators on S 4 11/35
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Exact Results for 't Hooft Loops in Gauge Theories ... - Solvay Institutes

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