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

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Introduction Problem Definitions Method Solution Result Step 5. Integrate over Y 0 Combination of exp(−S| Y0 ) and Z 1−loop factorizes nicely into 〈 ZT (B) 〉 = ∫ where and Z 1-loop,pole = ∫ da Z north · Z south · Z equator = da |Z north | 2 · Z equator Z north =Z cl (â(N), q) Z 1-loop,pole (â(N), im f ) Z south =Z cl (â(S), ¯q) Z 1-loop,pole (â(S), im f ) Z equator =Z 1-loop,eq (â(E), im f , B) , [ ] 1 Z cl (â, q) = exp 2πiτ Tr â 2 . 2ε 1 ε 2 ∏ ∏ NF ∏ [ f=1 w∈R G [ ( G α·â ) ( ε G 2 + α·â ε ( ) 1 + w·â ε − ˆm f ε G α )] 1/2 ( 1 − w·â ε )] + ˆm 1/2 f ε and Z 1-loop,eq Vasily Pestun Localization for ’t Hooft operators on S 4 30/35
Introduction Problem Definitions Method Solution Result Other components Y α : instanton corrections In the limit x → 0, up to the terms O(x 2 ) our Q complex in the neighborhood of the north pole is exactly as the one of the gauge theory on R 4 ε,ε [Nekrasov’02] . Hence the other components of the localization locus Y α are the point instantons F + = 0 sitting at the north pole as in [Nekrasov’02] . Vasily Pestun Localization for ’t Hooft operators on S 4 31/35
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Exact Results for 't Hooft Loops in Gauge Theories ... - Solvay Institutes

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