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 />
Excision property of the <strong>in</strong>dex/Atiya-S<strong>in</strong>ger theory<br />
To f<strong>in</strong>d <strong>in</strong>dex <strong>for</strong> transversally elliptic operator D on a manifold<br />
M under equivariant U(1) action R we can cut M <strong>in</strong>to three<br />
pieces<br />
• neighborhood of the north pole<br />
• neighborhood of the equator<br />
• neighborhood of the south pole<br />
and apply Atiyah-S<strong>in</strong>ger fixed po<strong>in</strong>t <strong>for</strong>mula <strong>for</strong> the <strong>in</strong>dex<br />
<strong>in</strong>d D(R) = ∑ p∈F<br />
tr E0 (p) R − tr E1 (p) R<br />
.<br />
det T Mp (1 − R)<br />
Vasily Pestun Localization <strong>for</strong> ’t <strong>Hooft</strong> operators on S 4 25/35
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