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 />
To f<strong>in</strong>d the ratio of determ<strong>in</strong>ants (equivariant Euler character)<br />
we consider the <strong>in</strong>dex of operator D (equivariant Chern<br />
character)<br />
<strong>in</strong>d D = tr KerD e R − tr CokerD e R<br />
read the weights of R and comb<strong>in</strong>e them <strong>in</strong>to determ<strong>in</strong>ant<br />
us<strong>in</strong>g the rule<br />
∑<br />
c j e w j(ε 1 ,ε 2 ,â, ˆm f ) → ∏ w j (ε 1 , ε 2 , â, ˆm f ) c j<br />
j<br />
j<br />
Recall that R = J + R + [Φ, ·]<br />
J is the SD spatial rotation<br />
R is the R-symmetry rotation<br />
[Φ, ·] is the gauge trans<strong>for</strong>mation.<br />
Vasily Pestun Localization <strong>for</strong> ’t <strong>Hooft</strong> operators on S 4 24/35