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 />
−(1+x 2 1−x 2 2−x 2 3)[D 1 Φ 9 ]−2x 1 x 2 [D 2 Φ 9 ]−2x 1 x 3 [D 3 Φ 9 ]−2x 2 [Dˆ4 Φ 9]<br />
− 2x 1 Φ 9 − 2x 1 x 3 F 12 + 2x 1 x 2 F 13 + (1 − x 2 1 + x 2 2 + x 2 3)F 23 − 2x 3 F 1ˆ4<br />
+ i(1 + |⃗x| 2 )K 1 + 2x 1 F 3ˆ4 = 0<br />
−(1−x 2 1+x 2 2−x 2 3)[D 2 Φ 9 ]−2x 1 x 2 [D 1 Φ 9 ]−2x 2 x 3 [D 3 Φ 9 ]+2x 1 [Dˆ4 Φ 9]<br />
− 2x 2 Φ 9 − 2x 2 x 3 F 12 − 2x 1 x 2 F 23 − (2 2 + x 2 1 − x 2 2 + x 2 3)F 13 − 2x 3 F 2ˆ4<br />
+ i(1 + |⃗x| 2 )K 2 + 2x 2 F 3ˆ4 = 0<br />
2x 1 x 3 [D 1 Φ 9 ] + 2x 2 x 3 [D 2 Φ 9 ] − (1 + x 2 1 + x 2 2 − x 2 3)[D 3 Φ 9 ] + 2x 3 Φ 9<br />
+ 4irΦ 0 + (1 − x 2 1 − x 2 2 + x 2 3)F 12 + 2x 1 x 3 F 23 − 2x 2 x 3 F 13<br />
− 2x 2 F 2ˆ4 − 2x 3F 3ˆ4 − 2x 1F 1ˆ4 + i ( 1 + |⃗x| 2) K 3 = 0<br />
Vasily Pestun Localization <strong>for</strong> ’t <strong>Hooft</strong> operators on S 4 19/35
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