Exact Results for 't Hooft Loops in Gauge Theories ... - Solvay Institutes
Exact Results for 't Hooft Loops in Gauge Theories ... - Solvay Institutes
Exact Results for 't Hooft Loops in Gauge Theories ... - Solvay Institutes
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Introduction Problem Def<strong>in</strong>itions Method Solution Result<br />
Step 5. Integrate over Y 0<br />
Comb<strong>in</strong>ation of exp(−S| Y0 ) and Z 1−loop factorizes nicely <strong>in</strong>to<br />
〈<br />
ZT (B)<br />
〉<br />
=<br />
∫<br />
where<br />
and<br />
Z 1-loop,pole =<br />
∫<br />
da Z north · Z south · Z equator =<br />
da |Z north | 2 · Z equator<br />
Z north =Z cl (â(N), q) Z 1-loop,pole (â(N), im f )<br />
Z south =Z cl (â(S), ¯q) Z 1-loop,pole (â(S), im f )<br />
Z equator =Z 1-loop,eq (â(E), im f , B) ,<br />
[ ]<br />
1<br />
Z cl (â, q) = exp 2πiτ Tr â 2 .<br />
2ε 1 ε 2<br />
∏<br />
∏ NF<br />
∏ [<br />
f=1 w∈R<br />
G<br />
[ (<br />
G<br />
α·â<br />
) (<br />
ε G 2 +<br />
α·â<br />
ε<br />
(<br />
)<br />
1 + w·â<br />
ε<br />
− ˆm f<br />
ε<br />
G<br />
α<br />
)] 1/2<br />
(<br />
1 − w·â<br />
ε<br />
)]<br />
+ ˆm 1/2<br />
f<br />
ε<br />
and Z 1-loop,eq Vasily Pestun Localization <strong>for</strong> ’t <strong>Hooft</strong> operators on S 4 30/35