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
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Introduction Problem Def<strong>in</strong>itions Method Solution Result<br />
Step 3. The one-loop determ<strong>in</strong>ant<br />
Denot<strong>in</strong>g the fields of even and odd statistics with a sub<strong>in</strong>dex e<br />
and o respectively, the Q multiplets are<br />
ˆQ · ϕ e,o = ˆϕ o,e<br />
ˆQ · ˆϕ o,e = R · ϕ e,o .<br />
and then<br />
ˆQ 2 · ϕ e,o = R · ϕ e,o ,<br />
We can show that the one-loop determ<strong>in</strong>ant is<br />
det CokerD vmR| o<br />
det KerD vmR| e<br />
· det CokerD hmR| o<br />
det KerD hmR| e<br />
.<br />
where D is a certa<strong>in</strong> (tranversally elliptic) differential operator<br />
def<strong>in</strong>ed from our tQV term.<br />
Vasily Pestun Localization <strong>for</strong> ’t <strong>Hooft</strong> operators on S 4 23/35
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