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

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Introduction Problem Definitions Method Solution Result Barnes G-function The double product can be regularized G(1 + z) = (2π) z/2 e −((1+γz2 )+z)/2 ∞∏ n=1 ( 1 + z ) n e −z+ z2 2n . (5.5) n and then the one-loop contribution from each pole is Z 1-loop,pole (â) = ∏ ( ) ( α · â G 1/2 G 1/2 2 + α · â ) ε ε α and recall that the gauge parameter â at the poles is (at θ = 0) â(N) = ia − B 2r â(S) = ia + B 2r , Vasily Pestun Localization for ’t Hooft operators on S 4 28/35
Introduction Problem Definitions Method Solution Result Contribution to Z 1−loop from equatior Skipping derivation, the answer (for vectormultiplet) Z 1-loop,eq (â, B) = ∏ α>0 [ ( (â sin πα · ε + B ))] −α·B (5.6) 2 Schematically, this comes from extra modes that appear near the equator in the singular monopole background. Vasily Pestun Localization for ’t Hooft operators on S 4 29/35
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Exact Results for 't Hooft Loops in Gauge Theories ... - Solvay Institutes

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