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

Introduction Problem Definitions Method Solution Result
Step 1
The equations are QΨ = 0, where
QΨ = 1 2 F mnΓ mn ε − 1 2 φ aΓ aµ ∇ µ ε + iK i Γ 8i+4 ε
For our Q, the equations interpolate between
• north pole: instanton equations F + = 0 and DΦ 9 = 0
• equator: Bogomolny equations DΦ 9 = ∗F in the space
transversal to the S 1 orbits and invariance along S 1
• south pole: anti-instanton equations F − = 0 and DΦ 9 = 0.
Vasily Pestun Localization for ’t Hooft operators on S 4 16/35