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

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Introduction Problem Definitions Method Solution Result Solution strategy We need to localize the path integral of N = 2 gauge theory on S 4 in the presence of ’t Hooft singularity. 0 Define the action S, the t’ Hooft operator T and the fermionic operator Q compatible with S and T 1 Find the localization loci Y α (solve QΨ = 0). 2 Compute exp(−S| Yα ) 3 Compute the determinant Z 1−loop [N Yα ] 4 Integrate over Y α and sum over α Vasily Pestun Localization for ’t Hooft operators on S 4 14/35
Introduction Problem Definitions Method Solution Result Step 0. The Q. The Q is defined by a conformal Killing spinor ε on S 4 ∇ µ ε = Γ µ˜ε In the R 4 conformal frame generic ε is ε = ˆε s + x µ Γ µˆε c We choose certain ε s (chiral right) and ε c (chiral right) and fix Q = Q ε such that Q 2 = J + R where J is a self-dual rotation of S 4 and R is R-symmery in OSp(2|4) North pole x = 0, ε is chiral right South pole x = ∞, ε is chiral left Vasily Pestun Localization for ’t Hooft operators on S 4 15/35
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Exact Results for 't Hooft Loops in Gauge Theories ... - Solvay Institutes

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